algebra.continued_fractions.computation.approximation_corollaries ⟷ Mathlib.Algebra.ContinuedFractions.Computation.ApproximationCorollaries

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,11 +3,11 @@ Copyright (c) 2021 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.Approximations
-import Mathbin.Algebra.ContinuedFractions.ConvergentsEquiv
-import Mathbin.Algebra.Order.Archimedean
-import Mathbin.Algebra.Algebra.Basic
-import Mathbin.Topology.Order.Basic
+import Algebra.ContinuedFractions.Computation.Approximations
+import Algebra.ContinuedFractions.ConvergentsEquiv
+import Algebra.Order.Archimedean
+import Algebra.Algebra.Basic
+import Topology.Order.Basic
 
 #align_import algebra.continued_fractions.computation.approximation_corollaries from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,11 +2,6 @@
 Copyright (c) 2021 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.approximation_corollaries
-! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.ContinuedFractions.Computation.Approximations
 import Mathbin.Algebra.ContinuedFractions.ConvergentsEquiv
@@ -14,6 +9,8 @@ import Mathbin.Algebra.Order.Archimedean
 import Mathbin.Algebra.Algebra.Basic
 import Mathbin.Topology.Order.Basic
 
+#align_import algebra.continued_fractions.computation.approximation_corollaries from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
+
 /-!
 # Corollaries From Approximation Lemmas (`algebra.continued_fractions.computation.approximations`)
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -54,32 +54,43 @@ open GeneralizedContinuedFraction (of)
 
 open GeneralizedContinuedFraction
 
+#print GeneralizedContinuedFraction.of_isSimpleContinuedFraction /-
 theorem GeneralizedContinuedFraction.of_isSimpleContinuedFraction :
     (of v).IsSimpleContinuedFraction := fun _ _ nth_part_num_eq =>
   of_part_num_eq_one nth_part_num_eq
 #align generalized_continued_fraction.of_is_simple_continued_fraction GeneralizedContinuedFraction.of_isSimpleContinuedFraction
+-/
 
+#print SimpleContinuedFraction.of /-
 /-- Creates the simple continued fraction of a value. -/
 def SimpleContinuedFraction.of : SimpleContinuedFraction K :=
   ⟨of v, GeneralizedContinuedFraction.of_isSimpleContinuedFraction v⟩
 #align simple_continued_fraction.of SimpleContinuedFraction.of
+-/
 
+#print SimpleContinuedFraction.of_isContinuedFraction /-
 theorem SimpleContinuedFraction.of_isContinuedFraction :
     (SimpleContinuedFraction.of v).IsContinuedFraction := fun _ denom nth_part_denom_eq =>
   lt_of_lt_of_le zero_lt_one (of_one_le_get?_part_denom nth_part_denom_eq)
 #align simple_continued_fraction.of_is_continued_fraction SimpleContinuedFraction.of_isContinuedFraction
+-/
 
+#print ContinuedFraction.of /-
 /-- Creates the continued fraction of a value. -/
 def ContinuedFraction.of : ContinuedFraction K :=
   ⟨SimpleContinuedFraction.of v, SimpleContinuedFraction.of_isContinuedFraction v⟩
 #align continued_fraction.of ContinuedFraction.of
+-/
 
 namespace GeneralizedContinuedFraction
 
+#print GeneralizedContinuedFraction.of_convergents_eq_convergents' /-
 theorem of_convergents_eq_convergents' : (of v).convergents = (of v).convergents' :=
   @ContinuedFraction.convergents_eq_convergents' _ _ (ContinuedFraction.of v)
 #align generalized_continued_fraction.of_convergents_eq_convergents' GeneralizedContinuedFraction.of_convergents_eq_convergents'
+-/
 
+#print GeneralizedContinuedFraction.convergents_succ /-
 /-- The recurrence relation for the `convergents` of the continued fraction expansion
 of an element `v` of `K` in terms of the convergents of the inverse of its fractional part.
 -/
@@ -87,6 +98,7 @@ theorem convergents_succ (n : ℕ) :
     (of v).convergents (n + 1) = ⌊v⌋ + 1 / (of (Int.fract v)⁻¹).convergents n := by
   rw [of_convergents_eq_convergents', convergents'_succ, of_convergents_eq_convergents']
 #align generalized_continued_fraction.convergents_succ GeneralizedContinuedFraction.convergents_succ
+-/
 
 section Convergence
 
@@ -101,6 +113,7 @@ variable [Archimedean K]
 
 open Nat
 
+#print GeneralizedContinuedFraction.of_convergence_epsilon /-
 theorem of_convergence_epsilon : ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v - (of v).convergents n| < ε :=
   by
   intro ε ε_pos
@@ -161,13 +174,16 @@ theorem of_convergence_epsilon : ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v
       _ ≤ B * nB :=
         mul_le_mul B_ineq nB_ineq (by exact_mod_cast (fib (n + 2)).zero_le) (le_of_lt zero_lt_B)
 #align generalized_continued_fraction.of_convergence_epsilon GeneralizedContinuedFraction.of_convergence_epsilon
+-/
 
 attribute [local instance] Preorder.topology
 
+#print GeneralizedContinuedFraction.of_convergence /-
 theorem of_convergence [OrderTopology K] :
     Filter.Tendsto (of v).convergents Filter.atTop <| nhds v := by
   simpa [LinearOrderedAddCommGroup.tendsto_nhds, abs_sub_comm] using of_convergence_epsilon v
 #align generalized_continued_fraction.of_convergence GeneralizedContinuedFraction.of_convergence
+-/
 
 end Convergence
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -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.approximation_corollaries
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Topology.Order.Basic
 /-!
 # Corollaries From Approximation Lemmas (`algebra.continued_fractions.computation.approximations`)
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Summary
 
 We show that the generalized_continued_fraction given by `generalized_continued_fraction.of` in fact

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -157,7 +157,6 @@ theorem of_convergence_epsilon : ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v
           (by exact_mod_cast (fib (n + 1)).zero_le))
       _ ≤ B * nB :=
         mul_le_mul B_ineq nB_ineq (by exact_mod_cast (fib (n + 2)).zero_le) (le_of_lt zero_lt_B)
-      
 #align generalized_continued_fraction.of_convergence_epsilon GeneralizedContinuedFraction.of_convergence_epsilon
 
 attribute [local instance] Preorder.topology

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -117,8 +117,7 @@ theorem of_convergence_epsilon : ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v
     let nB := g.denominators (n + 1)
     have abs_v_sub_conv_le : |v - g.convergents n| ≤ 1 / (B * nB) :=
       abs_sub_convergents_le not_terminated_at_n
-    suffices : 1 / (B * nB) < ε
-    exact lt_of_le_of_lt abs_v_sub_conv_le this
+    suffices : 1 / (B * nB) < ε; exact lt_of_le_of_lt abs_v_sub_conv_le this
     -- show that `0 < (B * nB)` and then multiply by `B * nB` to get rid of the division
     have nB_ineq : (fib (n + 2) : K) ≤ nB :=
       haveI : ¬g.terminated_at (n + 1 - 1) := not_terminated_at_n
@@ -135,8 +134,7 @@ theorem of_convergence_epsilon : ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v
         haveI : (0 : K) < fib (n + 2) := by exact_mod_cast fib_pos (n + 1).zero_lt_succ
         lt_of_lt_of_le this nB_ineq
       solve_by_elim [mul_pos]
-    suffices : 1 < ε * (B * nB)
-    exact (div_lt_iff zero_lt_mul_conts).right this
+    suffices : 1 < ε * (B * nB); exact (div_lt_iff zero_lt_mul_conts).right this
     -- use that `N ≥ n` was obtained from the archimedean property to show the following
     have one_lt_ε_mul_N : 1 < ε * n :=
       by
@@ -145,10 +143,9 @@ theorem of_convergence_epsilon : ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v
       have : ε * N' ≤ ε * n :=
         (mul_le_mul_left ε_pos).right (le_trans this (by exact_mod_cast n_ge_N))
       exact lt_of_lt_of_le one_lt_ε_mul_N' this
-    suffices : ε * n ≤ ε * (B * nB)
-    exact lt_of_lt_of_le one_lt_ε_mul_N this
+    suffices : ε * n ≤ ε * (B * nB); exact lt_of_lt_of_le one_lt_ε_mul_N this
     -- cancel `ε`
-    suffices : (n : K) ≤ B * nB
+    suffices : (n : K) ≤ B * nB;
     exact (mul_le_mul_left ε_pos).right this
     show (n : K) ≤ B * nB
     calc

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,14 +4,15 @@ 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.approximation_corollaries
-! leanprover-community/mathlib commit 2738d2ca56cbc63be80c3bd48e9ed90ad94e947d
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.ContinuedFractions.Computation.Approximations
 import Mathbin.Algebra.ContinuedFractions.ConvergentsEquiv
 import Mathbin.Algebra.Order.Archimedean
-import Mathbin.Topology.Algebra.Order.Field
+import Mathbin.Algebra.Algebra.Basic
+import Mathbin.Topology.Order.Basic
 
 /-!
 # Corollaries From Approximation Lemmas (`algebra.continued_fractions.computation.approximations`)

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -62,7 +62,7 @@ def SimpleContinuedFraction.of : SimpleContinuedFraction K :=
 
 theorem SimpleContinuedFraction.of_isContinuedFraction :
     (SimpleContinuedFraction.of v).IsContinuedFraction := fun _ denom nth_part_denom_eq =>
-  lt_of_lt_of_le zero_lt_one (of_one_le_nth_part_denom nth_part_denom_eq)
+  lt_of_lt_of_le zero_lt_one (of_one_le_get?_part_denom nth_part_denom_eq)
 #align simple_continued_fraction.of_is_continued_fraction SimpleContinuedFraction.of_isContinuedFraction
 
 /-- Creates the continued fraction of a value. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -155,8 +155,8 @@ theorem of_convergence_epsilon : ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v
       _ ≤ fib (n + 1) := by exact_mod_cast fib_le_fib_succ
       _ ≤ fib (n + 1) * fib (n + 1) := by exact_mod_cast (fib (n + 1)).le_mul_self
       _ ≤ fib (n + 1) * fib (n + 2) :=
-        mul_le_mul_of_nonneg_left (by exact_mod_cast fib_le_fib_succ)
-          (by exact_mod_cast (fib (n + 1)).zero_le)
+        (mul_le_mul_of_nonneg_left (by exact_mod_cast fib_le_fib_succ)
+          (by exact_mod_cast (fib (n + 1)).zero_le))
       _ ≤ B * nB :=
         mul_le_mul B_ineq nB_ineq (by exact_mod_cast (fib (n + 2)).zero_le) (le_of_lt zero_lt_B)
       

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

This splits up the file Mathlib/Topology/Order/Basic.lean (currently > 2000 lines) into several smaller files.

@@ -7,7 +7,7 @@ import Mathlib.Algebra.ContinuedFractions.Computation.Approximations
 import Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv
 import Mathlib.Algebra.Order.Archimedean
 import Mathlib.Tactic.GCongr
-import Mathlib.Topology.Order.Basic
+import Mathlib.Topology.Order.LeftRightNhds
 
 #align_import algebra.continued_fractions.computation.approximation_corollaries from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
 

Also fix GeneralizedContinuedFraction.of_convergence: it worked for the Preorder.topology only.

@@ -45,8 +45,8 @@ convergence, fractions
 variable {K : Type*} (v : K) [LinearOrderedField K] [FloorRing K]
 
 open GeneralizedContinuedFraction (of)
-
 open GeneralizedContinuedFraction
+open scoped Topology
 
 theorem GeneralizedContinuedFraction.of_isSimpleContinuedFraction :
     (of v).IsSimpleContinuedFraction := fun _ _ nth_part_num_eq =>
@@ -141,10 +141,8 @@ theorem of_convergence_epsilon :
       _ ≤ B * nB := by gcongr
 #align generalized_continued_fraction.of_convergence_epsilon GeneralizedContinuedFraction.of_convergence_epsilon
 
-attribute [local instance] Preorder.topology
-
-theorem of_convergence [OrderTopology K] :
-    Filter.Tendsto (of v).convergents Filter.atTop <| nhds v := by
+theorem of_convergence [TopologicalSpace K] [OrderTopology K] :
+    Filter.Tendsto (of v).convergents Filter.atTop <| 𝓝 v := by
   simpa [LinearOrderedAddCommGroup.tendsto_nhds, abs_sub_comm] using of_convergence_epsilon v
 #align generalized_continued_fraction.of_convergence GeneralizedContinuedFraction.of_convergence
 

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -6,7 +6,6 @@ Authors: Kevin Kappelmann
 import Mathlib.Algebra.ContinuedFractions.Computation.Approximations
 import Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv
 import Mathlib.Algebra.Order.Archimedean
-import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Tactic.GCongr
 import Mathlib.Topology.Order.Basic
 

See Zulip thread for the discussion.

@@ -123,8 +123,8 @@ theorem of_convergence_epsilon :
     have B_ineq : (fib (n + 1) : K) ≤ B :=
       haveI : ¬g.TerminatedAt (n - 1) := mt (terminated_stable n.pred_le) not_terminated_at_n
       succ_nth_fib_le_of_nth_denom (Or.inr this)
-    have zero_lt_B : 0 < B := B_ineq.trans_lt' $ mod_cast fib_pos.2 n.succ_pos
-    have nB_pos : 0 < nB := nB_ineq.trans_lt' $ mod_cast fib_pos.2 $ succ_pos _
+    have zero_lt_B : 0 < B := B_ineq.trans_lt' <| mod_cast fib_pos.2 n.succ_pos
+    have nB_pos : 0 < nB := nB_ineq.trans_lt' <| mod_cast fib_pos.2 <| succ_pos _
     have zero_lt_mul_conts : 0 < B * nB := by positivity
     suffices 1 < ε * (B * nB) from (div_lt_iff zero_lt_mul_conts).mpr this
     -- use that `N' ≥ n` was obtained from the archimedean property to show the following

@@ -99,7 +99,7 @@ open Nat
 theorem of_convergence_epsilon :
     ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v - (of v).convergents n| < ε := by
   intro ε ε_pos
-  -- use the archimedean property to obtian a suitable N
+  -- use the archimedean property to obtain a suitable N
   rcases (exists_nat_gt (1 / ε) : ∃ N' : ℕ, 1 / ε < N') with ⟨N', one_div_ε_lt_N'⟩
   let N := max N' 5
   -- set minimum to 5 to have N ≤ fib N work
@@ -115,7 +115,7 @@ theorem of_convergence_epsilon :
     let nB := g.denominators (n + 1)
     have abs_v_sub_conv_le : |v - g.convergents n| ≤ 1 / (B * nB) :=
       abs_sub_convergents_le not_terminated_at_n
-    suffices : 1 / (B * nB) < ε; exact lt_of_le_of_lt abs_v_sub_conv_le this
+    suffices 1 / (B * nB) < ε from lt_of_le_of_lt abs_v_sub_conv_le this
     -- show that `0 < (B * nB)` and then multiply by `B * nB` to get rid of the division
     have nB_ineq : (fib (n + 2) : K) ≤ nB :=
       haveI : ¬g.TerminatedAt (n + 1 - 1) := not_terminated_at_n
@@ -126,10 +126,10 @@ theorem of_convergence_epsilon :
     have zero_lt_B : 0 < B := B_ineq.trans_lt' $ mod_cast fib_pos.2 n.succ_pos
     have nB_pos : 0 < nB := nB_ineq.trans_lt' $ mod_cast fib_pos.2 $ succ_pos _
     have zero_lt_mul_conts : 0 < B * nB := by positivity
-    suffices : 1 < ε * (B * nB); exact (div_lt_iff zero_lt_mul_conts).mpr this
-    -- use that `N ≥ n` was obtained from the archimedean property to show the following
+    suffices 1 < ε * (B * nB) from (div_lt_iff zero_lt_mul_conts).mpr this
+    -- use that `N' ≥ n` was obtained from the archimedean property to show the following
     calc 1 < ε * (N' : K) := (div_lt_iff' ε_pos).mp one_div_ε_lt_N'
-      _ ≤  ε * (B * nB) := ?_
+      _ ≤ ε * (B * nB) := ?_
     -- cancel `ε`
     gcongr
     calc

Following on from previous gcongr golfing PRs #4702 and #4784.

This is a replacement for #7901: this round of golfs, first introduced there, there exposed some performance issues in gcongr, hopefully fixed by #8731, and I am opening a new PR so that the performance can be checked against current master rather than master at the time of #7901.

@@ -7,6 +7,7 @@ import Mathlib.Algebra.ContinuedFractions.Computation.Approximations
 import Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv
 import Mathlib.Algebra.Order.Archimedean
 import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Tactic.GCongr
 import Mathlib.Topology.Order.Basic
 
 #align_import algebra.continued_fractions.computation.approximation_corollaries from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
@@ -127,24 +128,18 @@ theorem of_convergence_epsilon :
     have zero_lt_mul_conts : 0 < B * nB := by positivity
     suffices : 1 < ε * (B * nB); exact (div_lt_iff zero_lt_mul_conts).mpr this
     -- use that `N ≥ n` was obtained from the archimedean property to show the following
-    have one_lt_ε_mul_N : 1 < ε * n := by
-      have one_lt_ε_mul_N' : 1 < ε * (N' : K) := (div_lt_iff' ε_pos).mp one_div_ε_lt_N'
-      have : (N' : K) ≤ N := mod_cast le_max_left _ _
-      have : ε * N' ≤ ε * n :=
-        (mul_le_mul_left ε_pos).mpr (le_trans this (mod_cast n_ge_N))
-      exact lt_of_lt_of_le one_lt_ε_mul_N' this
-    suffices : ε * n ≤ ε * (B * nB); exact lt_of_lt_of_le one_lt_ε_mul_N this
+    calc 1 < ε * (N' : K) := (div_lt_iff' ε_pos).mp one_div_ε_lt_N'
+      _ ≤  ε * (B * nB) := ?_
     -- cancel `ε`
-    suffices : (n : K) ≤ B * nB;
-    exact (mul_le_mul_left ε_pos).mpr this
-    show (n : K) ≤ B * nB
+    gcongr
     calc
-      (n : K) ≤ fib n := mod_cast le_fib_self <| le_trans (le_max_right N' 5) n_ge_N
-      _ ≤ fib (n + 1) := mod_cast fib_le_fib_succ
-      _ ≤ fib (n + 1) * fib (n + 1) := mod_cast (fib (n + 1)).le_mul_self
-      _ ≤ fib (n + 1) * fib (n + 2) :=
-            mul_le_mul_of_nonneg_left (mod_cast fib_le_fib_succ) (cast_nonneg _)
-      _ ≤ B * nB := mul_le_mul B_ineq nB_ineq (cast_nonneg _) zero_lt_B.le
+      (N' : K) ≤ (N : K) := by exact_mod_cast le_max_left _ _
+      _ ≤ n := by exact_mod_cast n_ge_N
+      _ ≤ fib n := by exact_mod_cast le_fib_self <| le_trans (le_max_right N' 5) n_ge_N
+      _ ≤ fib (n + 1) := by exact_mod_cast fib_le_fib_succ
+      _ ≤ fib (n + 1) * fib (n + 1) := by exact_mod_cast (fib (n + 1)).le_mul_self
+      _ ≤ fib (n + 1) * fib (n + 2) := by gcongr; exact_mod_cast fib_le_fib_succ
+      _ ≤ B * nB := by gcongr
 #align generalized_continued_fraction.of_convergence_epsilon GeneralizedContinuedFraction.of_convergence_epsilon
 
 attribute [local instance] Preorder.topology

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -109,7 +109,7 @@ theorem of_convergence_epsilon :
   · have : v = g.convergents n := of_correctness_of_terminatedAt terminated_at_n
     have : v - g.convergents n = 0 := sub_eq_zero.mpr this
     rw [this]
-    exact_mod_cast ε_pos
+    exact mod_cast ε_pos
   · let B := g.denominators n
     let nB := g.denominators (n + 1)
     have abs_v_sub_conv_le : |v - g.convergents n| ≤ 1 / (B * nB) :=
@@ -122,16 +122,16 @@ theorem of_convergence_epsilon :
     have B_ineq : (fib (n + 1) : K) ≤ B :=
       haveI : ¬g.TerminatedAt (n - 1) := mt (terminated_stable n.pred_le) not_terminated_at_n
       succ_nth_fib_le_of_nth_denom (Or.inr this)
-    have zero_lt_B : 0 < B := B_ineq.trans_lt' $ by exact_mod_cast fib_pos.2 n.succ_pos
-    have nB_pos : 0 < nB := nB_ineq.trans_lt' $ by exact_mod_cast fib_pos.2 $ succ_pos _
+    have zero_lt_B : 0 < B := B_ineq.trans_lt' $ mod_cast fib_pos.2 n.succ_pos
+    have nB_pos : 0 < nB := nB_ineq.trans_lt' $ mod_cast fib_pos.2 $ succ_pos _
     have zero_lt_mul_conts : 0 < B * nB := by positivity
     suffices : 1 < ε * (B * nB); exact (div_lt_iff zero_lt_mul_conts).mpr this
     -- use that `N ≥ n` was obtained from the archimedean property to show the following
     have one_lt_ε_mul_N : 1 < ε * n := by
       have one_lt_ε_mul_N' : 1 < ε * (N' : K) := (div_lt_iff' ε_pos).mp one_div_ε_lt_N'
-      have : (N' : K) ≤ N := by exact_mod_cast le_max_left _ _
+      have : (N' : K) ≤ N := mod_cast le_max_left _ _
       have : ε * N' ≤ ε * n :=
-        (mul_le_mul_left ε_pos).mpr (le_trans this (by exact_mod_cast n_ge_N))
+        (mul_le_mul_left ε_pos).mpr (le_trans this (mod_cast n_ge_N))
       exact lt_of_lt_of_le one_lt_ε_mul_N' this
     suffices : ε * n ≤ ε * (B * nB); exact lt_of_lt_of_le one_lt_ε_mul_N this
     -- cancel `ε`
@@ -139,11 +139,11 @@ theorem of_convergence_epsilon :
     exact (mul_le_mul_left ε_pos).mpr this
     show (n : K) ≤ B * nB
     calc
-      (n : K) ≤ fib n := by exact_mod_cast le_fib_self <| le_trans (le_max_right N' 5) n_ge_N
-      _ ≤ fib (n + 1) := by exact_mod_cast fib_le_fib_succ
-      _ ≤ fib (n + 1) * fib (n + 1) := by exact_mod_cast (fib (n + 1)).le_mul_self
+      (n : K) ≤ fib n := mod_cast le_fib_self <| le_trans (le_max_right N' 5) n_ge_N
+      _ ≤ fib (n + 1) := mod_cast fib_le_fib_succ
+      _ ≤ fib (n + 1) * fib (n + 1) := mod_cast (fib (n + 1)).le_mul_self
       _ ≤ fib (n + 1) * fib (n + 2) :=
-            mul_le_mul_of_nonneg_left (by exact_mod_cast fib_le_fib_succ) (cast_nonneg _)
+            mul_le_mul_of_nonneg_left (mod_cast fib_le_fib_succ) (cast_nonneg _)
       _ ≤ B * nB := mul_le_mul B_ineq nB_ineq (cast_nonneg _) zero_lt_B.le
 #align generalized_continued_fraction.of_convergence_epsilon GeneralizedContinuedFraction.of_convergence_epsilon
 

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -99,7 +99,7 @@ theorem of_convergence_epsilon :
     ∀ ε > (0 : K), ∃ N : ℕ, ∀ n ≥ N, |v - (of v).convergents n| < ε := by
   intro ε ε_pos
   -- use the archimedean property to obtian a suitable N
-  rcases(exists_nat_gt (1 / ε) : ∃ N' : ℕ, 1 / ε < N') with ⟨N', one_div_ε_lt_N'⟩
+  rcases (exists_nat_gt (1 / ε) : ∃ N' : ℕ, 1 / ε < N') with ⟨N', one_div_ε_lt_N'⟩
   let N := max N' 5
   -- set minimum to 5 to have N ≤ fib N work
   exists N

Prove Zeckendorf's theorem: Every natural number can be written uniquely as a sum of distinct non-consecutive Fibonacci numbers.

Instead of proving an ExistsUnique statement, I define an equivalence between natural numbers and Zeckendorf representations.

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -122,14 +122,9 @@ theorem of_convergence_epsilon :
     have B_ineq : (fib (n + 1) : K) ≤ B :=
       haveI : ¬g.TerminatedAt (n - 1) := mt (terminated_stable n.pred_le) not_terminated_at_n
       succ_nth_fib_le_of_nth_denom (Or.inr this)
-    have zero_lt_B : 0 < B :=
-      haveI : (0 : K) < fib (n + 1) := by exact_mod_cast fib_pos n.zero_lt_succ
-      lt_of_lt_of_le this B_ineq
-    have zero_lt_mul_conts : 0 < B * nB := by
-      have : 0 < nB :=
-        haveI : (0 : K) < fib (n + 2) := by exact_mod_cast fib_pos (n + 1).zero_lt_succ
-        lt_of_lt_of_le this nB_ineq
-      solve_by_elim [mul_pos]
+    have zero_lt_B : 0 < B := B_ineq.trans_lt' $ by exact_mod_cast fib_pos.2 n.succ_pos
+    have nB_pos : 0 < nB := nB_ineq.trans_lt' $ by exact_mod_cast fib_pos.2 $ succ_pos _
+    have zero_lt_mul_conts : 0 < B * nB := by positivity
     suffices : 1 < ε * (B * nB); exact (div_lt_iff zero_lt_mul_conts).mpr this
     -- use that `N ≥ n` was obtained from the archimedean property to show the following
     have one_lt_ε_mul_N : 1 < ε * n := by
@@ -148,10 +143,8 @@ theorem of_convergence_epsilon :
       _ ≤ fib (n + 1) := by exact_mod_cast fib_le_fib_succ
       _ ≤ fib (n + 1) * fib (n + 1) := by exact_mod_cast (fib (n + 1)).le_mul_self
       _ ≤ fib (n + 1) * fib (n + 2) :=
-        (mul_le_mul_of_nonneg_left (by exact_mod_cast fib_le_fib_succ)
-          (by exact_mod_cast (fib (n + 1)).zero_le))
-      _ ≤ B * nB :=
-        mul_le_mul B_ineq nB_ineq (by exact_mod_cast (fib (n + 2)).zero_le) (le_of_lt zero_lt_B)
+            mul_le_mul_of_nonneg_left (by exact_mod_cast fib_le_fib_succ) (cast_nonneg _)
+      _ ≤ B * nB := mul_le_mul B_ineq nB_ineq (cast_nonneg _) zero_lt_B.le
 #align generalized_continued_fraction.of_convergence_epsilon GeneralizedContinuedFraction.of_convergence_epsilon
 
 attribute [local instance] Preorder.topology

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -42,7 +42,7 @@ convergence, fractions
 -/
 
 
-variable {K : Type _} (v : K) [LinearOrderedField K] [FloorRing K]
+variable {K : Type*} (v : K) [LinearOrderedField K] [FloorRing K]
 
 open GeneralizedContinuedFraction (of)
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,11 +2,6 @@
 Copyright (c) 2021 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.approximation_corollaries
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.ContinuedFractions.Computation.Approximations
 import Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv
@@ -14,6 +9,8 @@ import Mathlib.Algebra.Order.Archimedean
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Topology.Order.Basic
 
+#align_import algebra.continued_fractions.computation.approximation_corollaries from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # Corollaries From Approximation Lemmas (`Algebra.ContinuedFractions.Computation.Approximations`)