algebra.continued_fractions.computation.correctness_terminating
⟷
Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -154,7 +154,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
cases this
have s_nth_eq : g.s.nth n = some ⟨1, ⌊ifp_n.fr⁻¹⌋⟩ :=
nth_of_eq_some_of_nth_int_fract_pair_stream_fr_ne_zero nth_stream_eq nth_fract_ne_zero
- rw [← ifp_n_fract_inv_eq_floor] at s_nth_eq
+ rw [← ifp_n_fract_inv_eq_floor] at s_nth_eq
suffices v = comp_exact_value ppconts pconts ifp_n.fr by
simpa [conts, continuants_aux, s_nth_eq, comp_exact_value, nth_fract_ne_zero] using this
exact IH nth_stream_eq
@@ -195,7 +195,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
comp_exact_value_correctness_of_stream_eq_some_aux_comp pA ppA ifp_succ_n_fr_ne_zero
have tmp_calc' :=
comp_exact_value_correctness_of_stream_eq_some_aux_comp pB ppB ifp_succ_n_fr_ne_zero
- rw [inv_eq_one_div] at tmp_calc tmp_calc'
+ rw [inv_eq_one_div] at tmp_calc tmp_calc'
have : Int.fract (1 / ifp_n.fr) ≠ 0 := by simpa using ifp_succ_n_fr_ne_zero
-- now unfold the recurrence one step and simplify both sides to arrive at the conclusion
field_simp [conts, comp_exact_value, continuants_aux_recurrence s_nth_eq ppconts_eq pconts_eq,
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,11 +3,11 @@ Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
-import Mathbin.Algebra.ContinuedFractions.Computation.Translations
-import Mathbin.Algebra.ContinuedFractions.TerminatedStable
-import Mathbin.Algebra.ContinuedFractions.ContinuantsRecurrence
-import Mathbin.Order.Filter.AtTopBot
-import Mathbin.Tactic.FieldSimp
+import Algebra.ContinuedFractions.Computation.Translations
+import Algebra.ContinuedFractions.TerminatedStable
+import Algebra.ContinuedFractions.ContinuantsRecurrence
+import Order.Filter.AtTopBot
+import Tactic.FieldSimp
#align_import algebra.continued_fractions.computation.correctness_terminating from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,11 +2,6 @@
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-
-! This file was ported from Lean 3 source module algebra.continued_fractions.computation.correctness_terminating
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.ContinuedFractions.Computation.Translations
import Mathbin.Algebra.ContinuedFractions.TerminatedStable
@@ -14,6 +9,8 @@ import Mathbin.Algebra.ContinuedFractions.ContinuantsRecurrence
import Mathbin.Order.Filter.AtTopBot
import Mathbin.Tactic.FieldSimp
+#align_import algebra.continued_fractions.computation.correctness_terminating from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
+
/-!
# Correctness of Terminating Continued Fraction Computations (`generalized_continued_fraction.of`)
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -82,12 +82,14 @@ protected def compExactValue (pconts conts : Pair K) (fr : K) : K :=
variable [FloorRing K]
+#print GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp /-
/-- Just a computational lemma we need for the next main proof. -/
protected theorem compExactValue_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
(fract_a_ne_zero : Int.fract a ≠ 0) :
((⌊a⌋ : K) * b + c) / Int.fract a + b = (b * a + c) / Int.fract a := by
field_simp [fract_a_ne_zero]; rw [Int.fract]; ring
#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp
+-/
open
GeneralizedContinuedFraction (compExactValue compExactValue_correctness_of_stream_eq_some_aux_comp)
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -128,7 +128,6 @@ theorem compExactValue_correctness_of_stream_eq_some :
calc
v = Int.fract v + ⌊v⌋ := by rw [Int.fract_add_floor]
_ = ⌊v⌋ := by simp [fract_eq_zero]
-
-- int.fract v ≠ 0; the claim then easily follows by unfolding a single computation step
·
field_simp [continuants_aux, next_continuants, next_numerator, next_denominator,
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -86,7 +86,7 @@ variable [FloorRing K]
protected theorem compExactValue_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
(fract_a_ne_zero : Int.fract a ≠ 0) :
((⌊a⌋ : K) * b + c) / Int.fract a + b = (b * a + c) / Int.fract a := by
- field_simp [fract_a_ne_zero] ; rw [Int.fract]; ring
+ field_simp [fract_a_ne_zero]; rw [Int.fract]; ring
#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp
open
@@ -156,7 +156,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
cases this
have s_nth_eq : g.s.nth n = some ⟨1, ⌊ifp_n.fr⁻¹⌋⟩ :=
nth_of_eq_some_of_nth_int_fract_pair_stream_fr_ne_zero nth_stream_eq nth_fract_ne_zero
- rw [← ifp_n_fract_inv_eq_floor] at s_nth_eq
+ rw [← ifp_n_fract_inv_eq_floor] at s_nth_eq
suffices v = comp_exact_value ppconts pconts ifp_n.fr by
simpa [conts, continuants_aux, s_nth_eq, comp_exact_value, nth_fract_ne_zero] using this
exact IH nth_stream_eq
@@ -197,7 +197,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
comp_exact_value_correctness_of_stream_eq_some_aux_comp pA ppA ifp_succ_n_fr_ne_zero
have tmp_calc' :=
comp_exact_value_correctness_of_stream_eq_some_aux_comp pB ppB ifp_succ_n_fr_ne_zero
- rw [inv_eq_one_div] at tmp_calc tmp_calc'
+ rw [inv_eq_one_div] at tmp_calc tmp_calc'
have : Int.fract (1 / ifp_n.fr) ≠ 0 := by simpa using ifp_succ_n_fr_ne_zero
-- now unfold the recurrence one step and simplify both sides to arrive at the conclusion
field_simp [conts, comp_exact_value, continuants_aux_recurrence s_nth_eq ppconts_eq pconts_eq,
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -82,12 +82,6 @@ protected def compExactValue (pconts conts : Pair K) (fr : K) : K :=
variable [FloorRing K]
-/- warning: generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp -> GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {K : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} K] [_inst_2 : FloorRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1))] {a : K} (b : K) (c : K), (Ne.{succ u1} K (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (LinearOrderedSemifield.toSemifield.{u1} K (LinearOrderedField.toLinearOrderedSemifield.{u1} K _inst_1)))))))) -> (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (LinearOrderedField.toDiv.{u1} K _inst_1)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1))))) (Int.floor.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (LinearOrderedField.toDiv.{u1} K _inst_1)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))) b a) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)))
-Case conversion may be inaccurate. Consider using '#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_compₓ'. -/
/-- Just a computational lemma we need for the next main proof. -/
protected theorem compExactValue_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
(fract_a_ne_zero : Int.fract a ≠ 0) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -91,11 +91,8 @@ Case conversion may be inaccurate. Consider using '#align generalized_continued_
/-- Just a computational lemma we need for the next main proof. -/
protected theorem compExactValue_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
(fract_a_ne_zero : Int.fract a ≠ 0) :
- ((⌊a⌋ : K) * b + c) / Int.fract a + b = (b * a + c) / Int.fract a :=
- by
- field_simp [fract_a_ne_zero]
- rw [Int.fract]
- ring
+ ((⌊a⌋ : K) * b + c) / Int.fract a + b = (b * a + c) / Int.fract a := by
+ field_simp [fract_a_ne_zero] ; rw [Int.fract]; ring
#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp
open
@@ -175,8 +172,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
comp_exact_value ppconts pconts ifp_n.fr = comp_exact_value pconts conts ifp_succ_n.fr
by
have : v = comp_exact_value ppconts pconts ifp_n.fr := IH nth_stream_eq
- conv_lhs => rw [this]
- assumption
+ conv_lhs => rw [this]; assumption
-- get the correspondence between ifp_n and ifp_succ_n
obtain ⟨ifp_n', nth_stream_eq', ifp_n_fract_ne_zero, ⟨refl⟩⟩ :
∃ ifp_n,
@@ -190,10 +186,9 @@ theorem compExactValue_correctness_of_stream_eq_some :
nth_of_eq_some_of_nth_int_fract_pair_stream_fr_ne_zero nth_stream_eq ifp_n_fract_ne_zero
-- the claim now follows by unfolding the definitions and tedious calculations
-- some shorthand notation
- let ppA := ppconts.a
+ let ppA := ppconts.a;
let ppB := ppconts.b
- let pA := pconts.a
- let pB := pconts.b
+ let pA := pconts.a; let pB := pconts.b
have :
comp_exact_value ppconts pconts ifp_n.fr =
(ppA + ifp_n.fr⁻¹ * pA) / (ppB + ifp_n.fr⁻¹ * pB) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26
@@ -82,24 +82,24 @@ protected def compExactValue (pconts conts : Pair K) (fr : K) : K :=
variable [FloorRing K]
-/- warning: generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp -> GeneralizedContinuedFraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp is a dubious translation:
+/- warning: generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp -> GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp is a dubious translation:
lean 3 declaration is
forall {K : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} K] [_inst_2 : FloorRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1))] {a : K} (b : K) (c : K), (Ne.{succ u1} K (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))))))))) -> (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int K (HasLiftT.mk.{1, succ u1} Int K (CoeTCₓ.coe.{1, succ u1} Int K (Int.castCoe.{u1} K (AddGroupWithOne.toHasIntCast.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1))))))))) (Int.floor.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) b a) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)))
but is expected to have type
forall {K : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} K] [_inst_2 : FloorRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1))] {a : K} (b : K) (c : K), (Ne.{succ u1} K (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (LinearOrderedSemifield.toSemifield.{u1} K (LinearOrderedField.toLinearOrderedSemifield.{u1} K _inst_1)))))))) -> (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (LinearOrderedField.toDiv.{u1} K _inst_1)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1))))) (Int.floor.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (LinearOrderedField.toDiv.{u1} K _inst_1)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))) b a) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)))
-Case conversion may be inaccurate. Consider using '#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.comp_exact_value_correctness_of_stream_eq_some_aux_compₓ'. -/
+Case conversion may be inaccurate. Consider using '#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_compₓ'. -/
/-- Just a computational lemma we need for the next main proof. -/
-protected theorem comp_exact_value_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
+protected theorem compExactValue_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
(fract_a_ne_zero : Int.fract a ≠ 0) :
((⌊a⌋ : K) * b + c) / Int.fract a + b = (b * a + c) / Int.fract a :=
by
field_simp [fract_a_ne_zero]
rw [Int.fract]
ring
-#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp
+#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp
open
- GeneralizedContinuedFraction (compExactValue comp_exact_value_correctness_of_stream_eq_some_aux_comp)
+ GeneralizedContinuedFraction (compExactValue compExactValue_correctness_of_stream_eq_some_aux_comp)
#print GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some /-
/-- Shows the correctness of `comp_exact_value` in case the continued fraction
mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
! This file was ported from Lean 3 source module algebra.continued_fractions.computation.correctness_terminating
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -17,6 +17,9 @@ import Mathbin.Tactic.FieldSimp
/-!
# Correctness of Terminating Continued Fraction Computations (`generalized_continued_fraction.of`)
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
## Summary
We show the correctness of the
mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
! This file was ported from Lean 3 source module algebra.continued_fractions.computation.correctness_terminating
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
+! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -17,9 +17,6 @@ import Mathbin.Tactic.FieldSimp
/-!
# Correctness of Terminating Continued Fraction Computations (`generalized_continued_fraction.of`)
-> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.
-
## Summary
We show the correctness of the
mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
! This file was ported from Lean 3 source module algebra.continued_fractions.computation.correctness_terminating
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -17,6 +17,9 @@ import Mathbin.Tactic.FieldSimp
/-!
# Correctness of Terminating Continued Fraction Computations (`generalized_continued_fraction.of`)
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
## Summary
We show the correctness of the
mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013
@@ -56,6 +56,7 @@ open GeneralizedContinuedFraction (of)
variable {K : Type _} [LinearOrderedField K] {v : K} {n : ℕ}
+#print GeneralizedContinuedFraction.compExactValue /-
/-- Given two continuants `pconts` and `conts` and a value `fr`, this function returns
- `conts.a / conts.b` if `fr = 0`
- `exact_conts.a / exact_conts.b` where `exact_conts = next_continuants 1 fr⁻¹ pconts conts`
@@ -74,9 +75,16 @@ protected def compExactValue (pconts conts : Pair K) (fr : K) : K :=
let exact_conts := nextContinuants 1 fr⁻¹ pconts conts
exact_conts.a / exact_conts.b
#align generalized_continued_fraction.comp_exact_value GeneralizedContinuedFraction.compExactValue
+-/
variable [FloorRing K]
+/- warning: generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp -> GeneralizedContinuedFraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp is a dubious translation:
+lean 3 declaration is
+ forall {K : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} K] [_inst_2 : FloorRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1))] {a : K} (b : K) (c : K), (Ne.{succ u1} K (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))))))))) -> (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int K (HasLiftT.mk.{1, succ u1} Int K (CoeTCₓ.coe.{1, succ u1} Int K (Int.castCoe.{u1} K (AddGroupWithOne.toHasIntCast.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1))))))))) (Int.floor.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K (LinearOrderedField.toField.{u1} K _inst_1)))))) b a) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)))
+but is expected to have type
+ forall {K : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} K] [_inst_2 : FloorRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1))] {a : K} (b : K) (c : K), (Ne.{succ u1} K (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (LinearOrderedSemifield.toSemifield.{u1} K (LinearOrderedField.toLinearOrderedSemifield.{u1} K _inst_1)))))))) -> (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (LinearOrderedField.toDiv.{u1} K _inst_1)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1))))) (Int.floor.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)) b) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (LinearOrderedField.toDiv.{u1} K _inst_1)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (StrictOrderedRing.toRing.{u1} K (LinearOrderedRing.toStrictOrderedRing.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)))))))) b a) c) (Int.fract.{u1} K (LinearOrderedCommRing.toLinearOrderedRing.{u1} K (LinearOrderedField.toLinearOrderedCommRing.{u1} K _inst_1)) _inst_2 a)))
+Case conversion may be inaccurate. Consider using '#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.comp_exact_value_correctness_of_stream_eq_some_aux_compₓ'. -/
/-- Just a computational lemma we need for the next main proof. -/
protected theorem comp_exact_value_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
(fract_a_ne_zero : Int.fract a ≠ 0) :
@@ -90,6 +98,7 @@ protected theorem comp_exact_value_correctness_of_stream_eq_some_aux_comp {a : K
open
GeneralizedContinuedFraction (compExactValue comp_exact_value_correctness_of_stream_eq_some_aux_comp)
+#print GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some /-
/-- Shows the correctness of `comp_exact_value` in case the continued fraction
`generalized_continued_fraction.of v` did not terminate at position `n`. That is, we obtain the
value `v` if we pass the two successive (auxiliary) continuants at positions `n` and `n + 1` as well
@@ -203,9 +212,11 @@ theorem compExactValue_correctness_of_stream_eq_some :
next_continuants, next_numerator, next_denominator, this, tmp_calc, tmp_calc']
ac_rfl
#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some
+-/
open GeneralizedContinuedFraction (of_terminatedAt_n_iff_succ_nth_intFractPair_stream_eq_none)
+#print GeneralizedContinuedFraction.of_correctness_of_nth_stream_eq_none /-
/-- The convergent of `generalized_continued_fraction.of v` at step `n - 1` is exactly `v` if the
`int_fract_pair.stream` of the corresponding continued fraction terminated at step `n`. -/
theorem of_correctness_of_nth_stream_eq_none (nth_stream_eq_none : IntFractPair.stream v n = none) :
@@ -235,7 +246,9 @@ theorem of_correctness_of_nth_stream_eq_none (nth_stream_eq_none : IntFractPair.
simpa [nth_stream_fr_eq_zero, comp_exact_value] using
comp_exact_value_correctness_of_stream_eq_some nth_stream_eq
#align generalized_continued_fraction.of_correctness_of_nth_stream_eq_none GeneralizedContinuedFraction.of_correctness_of_nth_stream_eq_none
+-/
+#print GeneralizedContinuedFraction.of_correctness_of_terminatedAt /-
/-- If `generalized_continued_fraction.of v` terminated at step `n`, then the `n`th convergent is
exactly `v`.
-/
@@ -245,7 +258,9 @@ theorem of_correctness_of_terminatedAt (terminated_at_n : (of v).TerminatedAt n)
of_terminatedAt_n_iff_succ_nth_intFractPair_stream_eq_none.left terminated_at_n
of_correctness_of_nth_stream_eq_none this
#align generalized_continued_fraction.of_correctness_of_terminated_at GeneralizedContinuedFraction.of_correctness_of_terminatedAt
+-/
+#print GeneralizedContinuedFraction.of_correctness_of_terminates /-
/-- If `generalized_continued_fraction.of v` terminates, then there is `n : ℕ` such that the `n`th
convergent is exactly `v`.
-/
@@ -254,9 +269,11 @@ theorem of_correctness_of_terminates (terminates : (of v).Terminates) :
Exists.elim terminates fun n terminated_at_n =>
Exists.intro n (of_correctness_of_terminatedAt terminated_at_n)
#align generalized_continued_fraction.of_correctness_of_terminates GeneralizedContinuedFraction.of_correctness_of_terminates
+-/
open Filter
+#print GeneralizedContinuedFraction.of_correctness_atTop_of_terminates /-
/-- If `generalized_continued_fraction.of v` terminates, then its convergents will eventually always
be `v`.
-/
@@ -271,6 +288,7 @@ theorem of_correctness_atTop_of_terminates (terminates : (of v).Terminates) :
rw [convergents_stable_of_terminated m_geq_n terminated_at_n]
exact of_correctness_of_terminated_at terminated_at_n
#align generalized_continued_fraction.of_correctness_at_top_of_terminates GeneralizedContinuedFraction.of_correctness_atTop_of_terminates
+-/
end GeneralizedContinuedFraction
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
mul
-div
cancellation lemmas (#11530)
Lemma names around cancellation of multiplication and division are a mess.
This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero
lemma name, the Group
lemma, the AddGroup
lemma name).
| Statement | New name | Old name | |
@@ -195,12 +195,12 @@ theorem compExactValue_correctness_of_stream_eq_some :
-- because `field_simp` is not as powerful
have hA : (↑⌊1 / ifp_n.fr⌋ * pA + ppA) + pA * f = pA * (1 / ifp_n.fr) + ppA := by
have := congrFun (congrArg HMul.hMul tmp_calc) f
- rwa [right_distrib, div_mul_cancel (h := f_ne_zero),
- div_mul_cancel (h := f_ne_zero)] at this
+ rwa [right_distrib, div_mul_cancel₀ (h := f_ne_zero),
+ div_mul_cancel₀ (h := f_ne_zero)] at this
have hB : (↑⌊1 / ifp_n.fr⌋ * pB + ppB) + pB * f = pB * (1 / ifp_n.fr) + ppB := by
have := congrFun (congrArg HMul.hMul tmp_calc') f
- rwa [right_distrib, div_mul_cancel (h := f_ne_zero),
- div_mul_cancel (h := f_ne_zero)] at this
+ rwa [right_distrib, div_mul_cancel₀ (h := f_ne_zero),
+ div_mul_cancel₀ (h := f_ne_zero)] at this
-- now unfold the recurrence one step and simplify both sides to arrive at the conclusion
dsimp only [conts, pconts, ppconts]
field_simp [compExactValue, continuantsAux_recurrence s_nth_eq ppconts_eq pconts_eq,
This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0
branch as we update to intermediate nightlies.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>
@@ -104,7 +104,7 @@ corresponds exactly to the one using the recurrence equation in `compExactValue`
theorem compExactValue_correctness_of_stream_eq_some :
∀ {ifp_n : IntFractPair K}, IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux <| n + 1) ifp_n.fr := by
- set g := of v with g_eq
+ let g := of v
induction' n with n IH
· intro ifp_zero stream_zero_eq
-- Nat.zero
@@ -135,7 +135,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_succ_n :=
IntFractPair.succ_nth_stream_eq_some_iff.1 succ_nth_stream_eq
-- introduce some notation
- set conts := g.continuantsAux (n + 2) with conts_eq
+ let conts := g.continuantsAux (n + 2)
set pconts := g.continuantsAux (n + 1) with pconts_eq
set ppconts := g.continuantsAux n with ppconts_eq
cases' Decidable.em (ifp_succ_n.fr = 0) with ifp_succ_n_fr_eq_zero ifp_succ_n_fr_ne_zero
@@ -151,7 +151,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero nth_stream_eq nth_fract_ne_zero
rw [← ifp_n_fract_inv_eq_floor] at s_nth_eq
suffices v = compExactValue ppconts pconts ifp_n.fr by
- simpa [continuantsAux, s_nth_eq, compExactValue, nth_fract_ne_zero] using this
+ simpa [conts, continuantsAux, s_nth_eq, compExactValue, nth_fract_ne_zero] using this
exact IH nth_stream_eq
-- ifp_succ_n.fr ≠ 0
· -- use the IH to show that the following equality suffices
@@ -172,15 +172,15 @@ theorem compExactValue_correctness_of_stream_eq_some :
get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero nth_stream_eq ifp_n_fract_ne_zero
-- the claim now follows by unfolding the definitions and tedious calculations
-- some shorthand notation
- set ppA := ppconts.a with ppA_eq
- set ppB := ppconts.b with ppB_eq
- set pA := pconts.a with pA_eq
- set pB := pconts.b with pB_eq
+ let ppA := ppconts.a
+ let ppB := ppconts.b
+ let pA := pconts.a
+ let pB := pconts.b
have : compExactValue ppconts pconts ifp_n.fr =
(ppA + ifp_n.fr⁻¹ * pA) / (ppB + ifp_n.fr⁻¹ * pB) := by
-- unfold compExactValue and the convergent computation once
field_simp [ifp_n_fract_ne_zero, compExactValue, nextContinuants, nextNumerator,
- nextDenominator]
+ nextDenominator, ppA, ppB]
ac_rfl
rw [this]
-- two calculations needed to show the claim
@@ -188,8 +188,8 @@ theorem compExactValue_correctness_of_stream_eq_some :
compExactValue_correctness_of_stream_eq_some_aux_comp pA ppA ifp_succ_n_fr_ne_zero
have tmp_calc' :=
compExactValue_correctness_of_stream_eq_some_aux_comp pB ppB ifp_succ_n_fr_ne_zero
- set f := Int.fract (1 / ifp_n.fr) with f_eq
- have f_ne_zero : f ≠ 0 := by simpa using ifp_succ_n_fr_ne_zero
+ let f := Int.fract (1 / ifp_n.fr)
+ have f_ne_zero : f ≠ 0 := by simpa [f] using ifp_succ_n_fr_ne_zero
rw [inv_eq_one_div] at tmp_calc tmp_calc'
-- Porting note: the `tmp_calc`s need to be massaged, and some processing after `ac_rfl` done,
-- because `field_simp` is not as powerful
@@ -202,13 +202,12 @@ theorem compExactValue_correctness_of_stream_eq_some :
rwa [right_distrib, div_mul_cancel (h := f_ne_zero),
div_mul_cancel (h := f_ne_zero)] at this
-- now unfold the recurrence one step and simplify both sides to arrive at the conclusion
- rw [ppA_eq, ppB_eq, pA_eq, pB_eq, conts_eq, pconts_eq, ppconts_eq, g_eq]
+ dsimp only [conts, pconts, ppconts]
field_simp [compExactValue, continuantsAux_recurrence s_nth_eq ppconts_eq pconts_eq,
nextContinuants, nextNumerator, nextDenominator]
have hfr : (IntFractPair.of (1 / ifp_n.fr)).fr = f := rfl
rw [one_div, if_neg _, ← one_div, hfr]
- · rw [f_eq]
- field_simp [hA, hB]
+ · field_simp [hA, hB]
ac_rfl
· rwa [inv_eq_one_div, hfr]
#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some
@@ -132,8 +132,8 @@ theorem compExactValue_correctness_of_stream_eq_some :
-- Nat.succ
obtain ⟨ifp_n, nth_stream_eq, nth_fract_ne_zero, -⟩ :
∃ ifp_n, IntFractPair.stream v n = some ifp_n ∧
- ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_succ_n
- exact IntFractPair.succ_nth_stream_eq_some_iff.1 succ_nth_stream_eq
+ ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_succ_n :=
+ IntFractPair.succ_nth_stream_eq_some_iff.1 succ_nth_stream_eq
-- introduce some notation
set conts := g.continuantsAux (n + 2) with conts_eq
set pconts := g.continuantsAux (n + 1) with pconts_eq
@@ -143,8 +143,8 @@ theorem compExactValue_correctness_of_stream_eq_some :
· suffices v = conts.a / conts.b by simpa [compExactValue, ifp_succ_n_fr_eq_zero]
-- use the IH and the fact that ifp_n.fr⁻¹ = ⌊ifp_n.fr⁻¹⌋ to prove this case
obtain ⟨ifp_n', nth_stream_eq', ifp_n_fract_inv_eq_floor⟩ :
- ∃ ifp_n, IntFractPair.stream v n = some ifp_n ∧ ifp_n.fr⁻¹ = ⌊ifp_n.fr⁻¹⌋
- exact IntFractPair.exists_succ_nth_stream_of_fr_zero succ_nth_stream_eq ifp_succ_n_fr_eq_zero
+ ∃ ifp_n, IntFractPair.stream v n = some ifp_n ∧ ifp_n.fr⁻¹ = ⌊ifp_n.fr⁻¹⌋ :=
+ IntFractPair.exists_succ_nth_stream_of_fr_zero succ_nth_stream_eq ifp_succ_n_fr_eq_zero
have : ifp_n' = ifp_n := by injection Eq.trans nth_stream_eq'.symm nth_stream_eq
cases this
have s_nth_eq : g.s.get? n = some ⟨1, ⌊ifp_n.fr⁻¹⌋⟩ :=
@@ -163,8 +163,8 @@ theorem compExactValue_correctness_of_stream_eq_some :
-- get the correspondence between ifp_n and ifp_succ_n
obtain ⟨ifp_n', nth_stream_eq', ifp_n_fract_ne_zero, ⟨refl⟩⟩ :
∃ ifp_n, IntFractPair.stream v n = some ifp_n ∧
- ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_succ_n
- exact IntFractPair.succ_nth_stream_eq_some_iff.1 succ_nth_stream_eq
+ ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_succ_n :=
+ IntFractPair.succ_nth_stream_eq_some_iff.1 succ_nth_stream_eq
have : ifp_n' = ifp_n := by injection Eq.trans nth_stream_eq'.symm nth_stream_eq
cases this
-- get the correspondence between ifp_n and g.s.nth n
@@ -270,8 +270,7 @@ be `v`.
theorem of_correctness_atTop_of_terminates (terminates : (of v).Terminates) :
∀ᶠ n in atTop, v = (of v).convergents n := by
rw [eventually_atTop]
- obtain ⟨n, terminated_at_n⟩ : ∃ n, (of v).TerminatedAt n
- exact terminates
+ obtain ⟨n, terminated_at_n⟩ : ∃ n, (of v).TerminatedAt n := terminates
use n
intro m m_geq_n
rw [convergents_stable_of_terminated m_geq_n terminated_at_n]
This is an attempt to fix Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean
.
I replaced some let
s by set
s and used rewrites when field_simp
seemed to unfold the lets.
@@ -104,7 +104,7 @@ corresponds exactly to the one using the recurrence equation in `compExactValue`
theorem compExactValue_correctness_of_stream_eq_some :
∀ {ifp_n : IntFractPair K}, IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux <| n + 1) ifp_n.fr := by
- let g := of v
+ set g := of v with g_eq
induction' n with n IH
· intro ifp_zero stream_zero_eq
-- Nat.zero
@@ -135,7 +135,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_succ_n
exact IntFractPair.succ_nth_stream_eq_some_iff.1 succ_nth_stream_eq
-- introduce some notation
- let conts := g.continuantsAux (n + 2)
+ set conts := g.continuantsAux (n + 2) with conts_eq
set pconts := g.continuantsAux (n + 1) with pconts_eq
set ppconts := g.continuantsAux n with ppconts_eq
cases' Decidable.em (ifp_succ_n.fr = 0) with ifp_succ_n_fr_eq_zero ifp_succ_n_fr_ne_zero
@@ -172,10 +172,10 @@ theorem compExactValue_correctness_of_stream_eq_some :
get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero nth_stream_eq ifp_n_fract_ne_zero
-- the claim now follows by unfolding the definitions and tedious calculations
-- some shorthand notation
- let ppA := ppconts.a
- let ppB := ppconts.b
- let pA := pconts.a
- let pB := pconts.b
+ set ppA := ppconts.a with ppA_eq
+ set ppB := ppconts.b with ppB_eq
+ set pA := pconts.a with pA_eq
+ set pB := pconts.b with pB_eq
have : compExactValue ppconts pconts ifp_n.fr =
(ppA + ifp_n.fr⁻¹ * pA) / (ppB + ifp_n.fr⁻¹ * pB) := by
-- unfold compExactValue and the convergent computation once
@@ -188,7 +188,7 @@ theorem compExactValue_correctness_of_stream_eq_some :
compExactValue_correctness_of_stream_eq_some_aux_comp pA ppA ifp_succ_n_fr_ne_zero
have tmp_calc' :=
compExactValue_correctness_of_stream_eq_some_aux_comp pB ppB ifp_succ_n_fr_ne_zero
- let f := Int.fract (1 / ifp_n.fr)
+ set f := Int.fract (1 / ifp_n.fr) with f_eq
have f_ne_zero : f ≠ 0 := by simpa using ifp_succ_n_fr_ne_zero
rw [inv_eq_one_div] at tmp_calc tmp_calc'
-- Porting note: the `tmp_calc`s need to be massaged, and some processing after `ac_rfl` done,
@@ -202,11 +202,13 @@ theorem compExactValue_correctness_of_stream_eq_some :
rwa [right_distrib, div_mul_cancel (h := f_ne_zero),
div_mul_cancel (h := f_ne_zero)] at this
-- now unfold the recurrence one step and simplify both sides to arrive at the conclusion
+ rw [ppA_eq, ppB_eq, pA_eq, pB_eq, conts_eq, pconts_eq, ppconts_eq, g_eq]
field_simp [compExactValue, continuantsAux_recurrence s_nth_eq ppconts_eq pconts_eq,
nextContinuants, nextNumerator, nextDenominator]
have hfr : (IntFractPair.of (1 / ifp_n.fr)).fr = f := rfl
rw [one_div, if_neg _, ← one_div, hfr]
- · field_simp [hA, hB]
+ · rw [f_eq]
+ field_simp [hA, hB]
ac_rfl
· rwa [inv_eq_one_div, hfr]
#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some
@@ -206,9 +206,9 @@ theorem compExactValue_correctness_of_stream_eq_some :
nextContinuants, nextNumerator, nextDenominator]
have hfr : (IntFractPair.of (1 / ifp_n.fr)).fr = f := rfl
rw [one_div, if_neg _, ← one_div, hfr]
- field_simp [hA, hB]
- ac_rfl
- rwa [inv_eq_one_div, hfr]
+ · field_simp [hA, hB]
+ ac_rfl
+ · rwa [inv_eq_one_div, hfr]
#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some
open GeneralizedContinuedFraction (of_terminatedAt_n_iff_succ_nth_intFractPair_stream_eq_none)
I appreciate that this is "going backwards" in the sense of requiring more explicit imports of tactics (and making it more likely that users writing new files will need to import tactics rather than finding them already available).
However it's useful for me while I'm intensively working on refactoring and upstreaming tactics if I can minimise the dependencies between tactics. I'm very much aware that in the long run we don't want users to have to manage imports of tactics, and I am definitely going to tidy this all up again once I'm finished with this project!
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -8,6 +8,7 @@ import Mathlib.Algebra.ContinuedFractions.TerminatedStable
import Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence
import Mathlib.Order.Filter.AtTopBot
import Mathlib.Tactic.FieldSimp
+import Mathlib.Tactic.Ring
#align_import algebra.continued_fractions.computation.correctness_terminating from "leanprover-community/mathlib"@"d6814c584384ddf2825ff038e868451a7c956f31"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -51,7 +51,7 @@ namespace GeneralizedContinuedFraction
open GeneralizedContinuedFraction (of)
-variable {K : Type _} [LinearOrderedField K] {v : K} {n : ℕ}
+variable {K : Type*} [LinearOrderedField K] {v : K} {n : ℕ}
/-- Given two continuants `pconts` and `conts` and a value `fr`, this function returns
- `conts.a / conts.b` if `fr = 0`
@@ -2,11 +2,6 @@
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-
-! This file was ported from Lean 3 source module algebra.continued_fractions.computation.correctness_terminating
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.ContinuedFractions.Computation.Translations
import Mathlib.Algebra.ContinuedFractions.TerminatedStable
@@ -14,6 +9,8 @@ import Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence
import Mathlib.Order.Filter.AtTopBot
import Mathlib.Tactic.FieldSimp
+#align_import algebra.continued_fractions.computation.correctness_terminating from "leanprover-community/mathlib"@"d6814c584384ddf2825ff038e868451a7c956f31"
+
/-!
# Correctness of Terminating Continued Fraction Computations (`GeneralizedContinuedFraction.of`)
@@ -61,7 +61,7 @@ variable {K : Type _} [LinearOrderedField K] {v : K} {n : ℕ}
- `exact_conts.a / exact_conts.b` where `exact_conts = nextContinuants 1 fr⁻¹ pconts conts`
otherwise.
-This function can be used to compute the exact value approxmated by a continued fraction
+This function can be used to compute the exact value approximated by a continued fraction
`GeneralizedContinuedFraction.of v` as described in lemma
`compExactValue_correctness_of_stream_eq_some`.
-/
@@ -15,7 +15,7 @@ import Mathlib.Order.Filter.AtTopBot
import Mathlib.Tactic.FieldSimp
/-!
-# Correctness of Terminating Continued Fraction Computations (`generalized_continued_fraction.of`)
+# Correctness of Terminating Continued Fraction Computations (`GeneralizedContinuedFraction.of`)
## Summary
@@ -77,16 +77,16 @@ protected def compExactValue (pconts conts : Pair K) (fr : K) : K :=
variable [FloorRing K]
/-- Just a computational lemma we need for the next main proof. -/
-protected theorem comp_exact_value_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
+protected theorem compExactValue_correctness_of_stream_eq_some_aux_comp {a : K} (b c : K)
(fract_a_ne_zero : Int.fract a ≠ 0) :
((⌊a⌋ : K) * b + c) / Int.fract a + b = (b * a + c) / Int.fract a := by
field_simp [fract_a_ne_zero]
rw [Int.fract]
ring
-#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp
+#align generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp
open GeneralizedContinuedFraction
- (compExactValue comp_exact_value_correctness_of_stream_eq_some_aux_comp)
+ (compExactValue compExactValue_correctness_of_stream_eq_some_aux_comp)
/-- Shows the correctness of `compExactValue` in case the continued fraction
`GeneralizedContinuedFraction.of v` did not terminate at position `n`. That is, we obtain the
@@ -187,9 +187,9 @@ theorem compExactValue_correctness_of_stream_eq_some :
rw [this]
-- two calculations needed to show the claim
have tmp_calc :=
- comp_exact_value_correctness_of_stream_eq_some_aux_comp pA ppA ifp_succ_n_fr_ne_zero
+ compExactValue_correctness_of_stream_eq_some_aux_comp pA ppA ifp_succ_n_fr_ne_zero
have tmp_calc' :=
- comp_exact_value_correctness_of_stream_eq_some_aux_comp pB ppB ifp_succ_n_fr_ne_zero
+ compExactValue_correctness_of_stream_eq_some_aux_comp pB ppB ifp_succ_n_fr_ne_zero
let f := Int.fract (1 / ifp_n.fr)
have f_ne_zero : f ≠ 0 := by simpa using ifp_succ_n_fr_ne_zero
rw [inv_eq_one_div] at tmp_calc tmp_calc'
@@ -219,10 +219,10 @@ open GeneralizedContinuedFraction (of_terminatedAt_n_iff_succ_nth_intFractPair_s
`IntFractPair.stream` of the corresponding continued fraction terminated at step `n`. -/
theorem of_correctness_of_nth_stream_eq_none (nth_stream_eq_none : IntFractPair.stream v n = none) :
v = (of v).convergents (n - 1) := by
- induction' n with n IH
- case zero => contradiction
+ induction n with
+ | zero => contradiction
-- IntFractPair.stream v 0 ≠ none
- case succ =>
+ | succ n IH =>
let g := of v
change v = g.convergents n
have :
The unported dependencies are