data.nat.factorial.cast | Mathlib porting status

Changes since the initial port

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.

Changes in mathlib3

d50b12ae

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

69c6a5a1

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -74,7 +74,7 @@ theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=
   cases a
   · rw [zero_tsub, cast_zero, ascPochhammer_ne_zero_eval_zero _ two_ne_zero, MulZeroClass.zero_mul]
   ·
-    rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, ascPochhammer_succ_right,
+    rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel_right, ascPochhammer_succ_right,
       ascPochhammer_one, Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add,
       Polynomial.eval_X, cast_one, Polynomial.eval_one]
 #align nat.cast_desc_factorial_two Nat.cast_descFactorial_two

69c6a5a1

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 -/
-import Mathbin.RingTheory.Polynomial.Pochhammer
+import RingTheory.Polynomial.Pochhammer
 
 #align_import data.nat.factorial.cast from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"

69c6a5a1

bump to nightly-2023-09-14-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

4e7aae4f

Diff

@@ -34,15 +34,15 @@ section Semiring
 variable [Semiring S] (a b : ℕ)
 
 #print Nat.cast_ascFactorial /-
-theorem cast_ascFactorial : (a.ascFactorial b : S) = (pochhammer S b).eval (a + 1) := by
-  rw [← pochhammer_nat_eq_ascFactorial, pochhammer_eval_cast, Nat.cast_add, Nat.cast_one]
+theorem cast_ascFactorial : (a.ascFactorial b : S) = (ascPochhammer S b).eval (a + 1) := by
+  rw [← ascPochhammer_nat_eq_ascFactorial, ascPochhammer_eval_cast, Nat.cast_add, Nat.cast_one]
 #align nat.cast_asc_factorial Nat.cast_ascFactorial
 -/
 
 #print Nat.cast_descFactorial /-
-theorem cast_descFactorial : (a.descFactorial b : S) = (pochhammer S b).eval (a - (b - 1) : ℕ) :=
+theorem cast_descFactorial : (a.descFactorial b : S) = (ascPochhammer S b).eval (a - (b - 1) : ℕ) :=
   by
-  rw [← pochhammer_eval_cast, pochhammer_nat_eq_descFactorial]
+  rw [← ascPochhammer_eval_cast, ascPochhammer_nat_eq_descFactorial]
   cases b
   · simp_rw [desc_factorial_zero]
   simp_rw [add_succ, succ_sub_one]
@@ -54,7 +54,7 @@ theorem cast_descFactorial : (a.descFactorial b : S) = (pochhammer S b).eval (a
 -/
 
 #print Nat.cast_factorial /-
-theorem cast_factorial : (a ! : S) = (pochhammer S a).eval 1 := by
+theorem cast_factorial : (a ! : S) = (ascPochhammer S a).eval 1 := by
   rw [← zero_asc_factorial, cast_asc_factorial, cast_zero, zero_add]
 #align nat.cast_factorial Nat.cast_factorial
 -/
@@ -72,11 +72,11 @@ theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=
   by
   rw [cast_desc_factorial]
   cases a
-  · rw [zero_tsub, cast_zero, pochhammer_ne_zero_eval_zero _ two_ne_zero, MulZeroClass.zero_mul]
+  · rw [zero_tsub, cast_zero, ascPochhammer_ne_zero_eval_zero _ two_ne_zero, MulZeroClass.zero_mul]
   ·
-    rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, pochhammer_succ_right, pochhammer_one,
-      Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add, Polynomial.eval_X, cast_one,
-      Polynomial.eval_one]
+    rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, ascPochhammer_succ_right,
+      ascPochhammer_one, Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add,
+      Polynomial.eval_X, cast_one, Polynomial.eval_one]
 #align nat.cast_desc_factorial_two Nat.cast_descFactorial_two
 -/

69c6a5a1

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module data.nat.factorial.cast
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Polynomial.Pochhammer
 
+#align_import data.nat.factorial.cast from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
 /-!
 # Cast of factorials

69c6a5a1

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -36,9 +36,11 @@ section Semiring
 
 variable [Semiring S] (a b : ℕ)
 
+#print Nat.cast_ascFactorial /-
 theorem cast_ascFactorial : (a.ascFactorial b : S) = (pochhammer S b).eval (a + 1) := by
   rw [← pochhammer_nat_eq_ascFactorial, pochhammer_eval_cast, Nat.cast_add, Nat.cast_one]
 #align nat.cast_asc_factorial Nat.cast_ascFactorial
+-/
 
 #print Nat.cast_descFactorial /-
 theorem cast_descFactorial : (a.descFactorial b : S) = (pochhammer S b).eval (a - (b - 1) : ℕ) :=
@@ -66,6 +68,7 @@ section Ring
 
 variable [Ring S] (a b : ℕ)
 
+#print Nat.cast_descFactorial_two /-
 /-- Convenience lemma. The `a - 1` is not using truncated subtraction, as opposed to the definition
 of `nat.desc_factorial` as a natural. -/
 theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=
@@ -78,6 +81,7 @@ theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=
       Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add, Polynomial.eval_X, cast_one,
       Polynomial.eval_one]
 #align nat.cast_desc_factorial_two Nat.cast_descFactorial_two
+-/
 
 end Ring

69c6a5a1

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ to `↑a - 1`, the other factor is `0` anyway.
 -/
 
 
-open Nat
+open scoped Nat
 
 variable (S : Type _)

69c6a5a1

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -36,12 +36,6 @@ section Semiring
 
 variable [Semiring S] (a b : ℕ)
 
-/- warning: nat.cast_asc_factorial -> Nat.cast_ascFactorial is a dubious translation:
-lean 3 declaration is
-  forall (S : Type.{u1}) [_inst_1 : Semiring.{u1} S] (a : Nat) (b : Nat), Eq.{succ u1} S ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1))))))) (Nat.ascFactorial a b)) (Polynomial.eval.{u1} S _inst_1 (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1))))))) a) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1)))))))) (pochhammer.{u1} S _inst_1 b))
-but is expected to have type
-  forall (S : Type.{u1}) [_inst_1 : Semiring.{u1} S] (a : Nat) (b : Nat), Eq.{succ u1} S (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_1) (Nat.ascFactorial a b)) (Polynomial.eval.{u1} S _inst_1 (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_1) a) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S _inst_1)))) (pochhammer.{u1} S _inst_1 b))
-Case conversion may be inaccurate. Consider using '#align nat.cast_asc_factorial Nat.cast_ascFactorialₓ'. -/
 theorem cast_ascFactorial : (a.ascFactorial b : S) = (pochhammer S b).eval (a + 1) := by
   rw [← pochhammer_nat_eq_ascFactorial, pochhammer_eval_cast, Nat.cast_add, Nat.cast_one]
 #align nat.cast_asc_factorial Nat.cast_ascFactorial
@@ -72,12 +66,6 @@ section Ring
 
 variable [Ring S] (a b : ℕ)
 
-/- warning: nat.cast_desc_factorial_two -> Nat.cast_descFactorial_two is a dubious translation:
-lean 3 declaration is
-  forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) a) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1)))))))))
-but is expected to have type
-  forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (Ring.toSemiring.{u1} S _inst_1)) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (Ring.toSemiring.{u1} S _inst_1)) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S _inst_1)) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (Ring.toSemiring.{u1} S _inst_1)) a) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (Ring.toSemiring.{u1} S _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align nat.cast_desc_factorial_two Nat.cast_descFactorial_twoₓ'. -/
 /-- Convenience lemma. The `a - 1` is not using truncated subtraction, as opposed to the definition
 of `nat.desc_factorial` as a natural. -/
 theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=

69c6a5a1

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -76,7 +76,7 @@ variable [Ring S] (a b : ℕ)
 lean 3 declaration is
   forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) a) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1)))))))))
 but is expected to have type
-  forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S _inst_1)) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) a) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))
+  forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (Ring.toSemiring.{u1} S _inst_1)) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (Ring.toSemiring.{u1} S _inst_1)) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S _inst_1)) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (Ring.toSemiring.{u1} S _inst_1)) a) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (Ring.toSemiring.{u1} S _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align nat.cast_desc_factorial_two Nat.cast_descFactorial_twoₓ'. -/
 /-- Convenience lemma. The `a - 1` is not using truncated subtraction, as opposed to the definition
 of `nat.desc_factorial` as a natural. -/

69c6a5a1

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -74,7 +74,7 @@ variable [Ring S] (a b : ℕ)
 
 /- warning: nat.cast_desc_factorial_two -> Nat.cast_descFactorial_two is a dubious translation:
 lean 3 declaration is
-  forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))) a) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))))))))
+  forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1))))))) a) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S _inst_1)))))))))
 but is expected to have type
   forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S _inst_1)) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) a) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align nat.cast_desc_factorial_two Nat.cast_descFactorial_twoₓ'. -/

69c6a5a1

bump to nightly-2023-03-14-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

d4b38a42

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 
 ! This file was ported from Lean 3 source module data.nat.factorial.cast
-! leanprover-community/mathlib commit d50b12ae8e2bd910d08a94823976adae9825718b
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.Polynomial.Pochhammer
 /-!
 # Cast of factorials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file allows calculating factorials (including ascending and descending ones) as elements of a
 semiring.

d50b12ae

bump to nightly-2023-03-11-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

1d00e3b6

Diff

@@ -33,10 +33,17 @@ section Semiring
 
 variable [Semiring S] (a b : ℕ)
 
+/- warning: nat.cast_asc_factorial -> Nat.cast_ascFactorial is a dubious translation:
+lean 3 declaration is
+  forall (S : Type.{u1}) [_inst_1 : Semiring.{u1} S] (a : Nat) (b : Nat), Eq.{succ u1} S ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1))))))) (Nat.ascFactorial a b)) (Polynomial.eval.{u1} S _inst_1 (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1))))))) a) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1)))))))) (pochhammer.{u1} S _inst_1 b))
+but is expected to have type
+  forall (S : Type.{u1}) [_inst_1 : Semiring.{u1} S] (a : Nat) (b : Nat), Eq.{succ u1} S (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_1) (Nat.ascFactorial a b)) (Polynomial.eval.{u1} S _inst_1 (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_1))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_1) a) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S _inst_1)))) (pochhammer.{u1} S _inst_1 b))
+Case conversion may be inaccurate. Consider using '#align nat.cast_asc_factorial Nat.cast_ascFactorialₓ'. -/
 theorem cast_ascFactorial : (a.ascFactorial b : S) = (pochhammer S b).eval (a + 1) := by
   rw [← pochhammer_nat_eq_ascFactorial, pochhammer_eval_cast, Nat.cast_add, Nat.cast_one]
 #align nat.cast_asc_factorial Nat.cast_ascFactorial
 
+#print Nat.cast_descFactorial /-
 theorem cast_descFactorial : (a.descFactorial b : S) = (pochhammer S b).eval (a - (b - 1) : ℕ) :=
   by
   rw [← pochhammer_eval_cast, pochhammer_nat_eq_descFactorial]
@@ -48,10 +55,13 @@ theorem cast_descFactorial : (a.descFactorial b : S) = (pochhammer S b).eval (a
     rw [tsub_eq_zero_iff_le.mpr h, zero_add]
   · rw [tsub_add_cancel_of_le h]
 #align nat.cast_desc_factorial Nat.cast_descFactorial
+-/
 
+#print Nat.cast_factorial /-
 theorem cast_factorial : (a ! : S) = (pochhammer S a).eval 1 := by
   rw [← zero_asc_factorial, cast_asc_factorial, cast_zero, zero_add]
 #align nat.cast_factorial Nat.cast_factorial
+-/
 
 end Semiring
 
@@ -59,6 +69,12 @@ section Ring
 
 variable [Ring S] (a b : ℕ)
 
+/- warning: nat.cast_desc_factorial_two -> Nat.cast_descFactorial_two is a dubious translation:
+lean 3 declaration is
+  forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))) a) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))))))))
+but is expected to have type
+  forall (S : Type.{u1}) [_inst_1 : Ring.{u1} S] (a : Nat), Eq.{succ u1} S (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) (Nat.descFactorial a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) a) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S _inst_1)) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1)) a) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align nat.cast_desc_factorial_two Nat.cast_descFactorial_twoₓ'. -/
 /-- Convenience lemma. The `a - 1` is not using truncated subtraction, as opposed to the definition
 of `nat.desc_factorial` as a natural. -/
 theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=

d50b12ae

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -65,7 +65,7 @@ theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=
   by
   rw [cast_desc_factorial]
   cases a
-  · rw [zero_tsub, cast_zero, pochhammer_ne_zero_eval_zero _ two_ne_zero, zero_mul]
+  · rw [zero_tsub, cast_zero, pochhammer_ne_zero_eval_zero _ two_ne_zero, MulZeroClass.zero_mul]
   ·
     rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, pochhammer_succ_right, pochhammer_one,
       Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add, Polynomial.eval_X, cast_one,

d50b12ae

bump to nightly-2023-03-08-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

f7af4b63

Diff

@@ -68,7 +68,7 @@ theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=
   · rw [zero_tsub, cast_zero, pochhammer_ne_zero_eval_zero _ two_ne_zero, zero_mul]
   ·
     rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, pochhammer_succ_right, pochhammer_one,
-      Polynomial.X_mul, Polynomial.eval_mul_x, Polynomial.eval_add, Polynomial.eval_x, cast_one,
+      Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add, Polynomial.eval_X, cast_one,
       Polynomial.eval_one]
 #align nat.cast_desc_factorial_two Nat.cast_descFactorial_two

d50b12ae

bump to nightly-2023-03-08-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

422cc012

Diff

@@ -68,7 +68,7 @@ theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) :=
   · rw [zero_tsub, cast_zero, pochhammer_ne_zero_eval_zero _ two_ne_zero, zero_mul]
   ·
     rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, pochhammer_succ_right, pochhammer_one,
-      Polynomial.x_mul, Polynomial.eval_mul_x, Polynomial.eval_add, Polynomial.eval_x, cast_one,
+      Polynomial.X_mul, Polynomial.eval_mul_x, Polynomial.eval_add, Polynomial.eval_x, cast_one,
       Polynomial.eval_one]
 #align nat.cast_desc_factorial_two Nat.cast_descFactorial_two

d50b12ae

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

d50b12ae

chore: Rename 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).

4ea4a86a

Diff

@@ -64,7 +64,7 @@ theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) := by
   rw [cast_descFactorial]
   cases a
   · simp
-  · rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, ascPochhammer_succ_right,
+  · rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel_right, ascPochhammer_succ_right,
       ascPochhammer_one, Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add,
       Polynomial.eval_X, cast_one, Polynomial.eval_one]
 #align nat.cast_desc_factorial_two Nat.cast_descFactorial_two

d50b12ae

chore: shift Nat.ascFactorial down by one (#7965)

change ascending factorial function Nat.ascFactorial to agree with mathematical literature. This means Nat.ascFactorial n k becomes n (n + 1) ⋯ (n + k - 1) instead of (n + 1) ⋯ (n + k)

Co-authored-by: Johan Commelin <johan@commelin.net>

0c15e423

Diff

@@ -31,8 +31,8 @@ section Semiring
 variable [Semiring S] (a b : ℕ)
 
 -- Porting note: added type ascription around a + 1
-theorem cast_ascFactorial : (a.ascFactorial b : S) = (ascPochhammer S b).eval (a + 1 : S) := by
-  rw [← ascPochhammer_nat_eq_ascFactorial, ascPochhammer_eval_cast, Nat.cast_add, Nat.cast_one]
+theorem cast_ascFactorial : (a.ascFactorial b : S) = (ascPochhammer S b).eval (a : S) := by
+  rw [← ascPochhammer_nat_eq_ascFactorial, ascPochhammer_eval_cast]
 #align nat.cast_asc_factorial Nat.cast_ascFactorial
 
 -- Porting note: added type ascription around a - (b - 1)
@@ -49,7 +49,7 @@ theorem cast_descFactorial :
 #align nat.cast_desc_factorial Nat.cast_descFactorial
 
 theorem cast_factorial : (a ! : S) = (ascPochhammer S a).eval 1 := by
-  rw [← zero_ascFactorial, cast_ascFactorial, cast_zero, zero_add]
+  rw [← one_ascFactorial, cast_ascFactorial, cast_one]
 #align nat.cast_factorial Nat.cast_factorial
 
 end Semiring

d50b12ae

fix: patch for std4#203 (more sub lemmas for Nat) (#6216)

c159834a

Diff

@@ -41,7 +41,7 @@ theorem cast_descFactorial :
   rw [← ascPochhammer_eval_cast, ascPochhammer_nat_eq_descFactorial]
   induction' b with b
   · simp
-  · simp_rw [add_succ, succ_sub_one]
+  · simp_rw [add_succ, Nat.add_one_sub_one]
     obtain h | h := le_total a b
     · rw [descFactorial_of_lt (lt_succ_of_le h), descFactorial_of_lt (lt_succ_of_le _)]
       rw [tsub_eq_zero_iff_le.mpr h, zero_add]

d50b12ae

chore: rename pochhammer (#6917)

We rename pochhammer to ascPochhammer to prepare adding descPochhammer.

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

ae1eb5e7

Diff

@@ -31,13 +31,14 @@ section Semiring
 variable [Semiring S] (a b : ℕ)
 
 -- Porting note: added type ascription around a + 1
-theorem cast_ascFactorial : (a.ascFactorial b : S) = (pochhammer S b).eval (a + 1 : S) := by
-  rw [← pochhammer_nat_eq_ascFactorial, pochhammer_eval_cast, Nat.cast_add, Nat.cast_one]
+theorem cast_ascFactorial : (a.ascFactorial b : S) = (ascPochhammer S b).eval (a + 1 : S) := by
+  rw [← ascPochhammer_nat_eq_ascFactorial, ascPochhammer_eval_cast, Nat.cast_add, Nat.cast_one]
 #align nat.cast_asc_factorial Nat.cast_ascFactorial
 
 -- Porting note: added type ascription around a - (b - 1)
-theorem cast_descFactorial : (a.descFactorial b : S) = (pochhammer S b).eval (a - (b - 1) : S) := by
-  rw [← pochhammer_eval_cast, pochhammer_nat_eq_descFactorial]
+theorem cast_descFactorial :
+    (a.descFactorial b : S) = (ascPochhammer S b).eval (a - (b - 1) : S) := by
+  rw [← ascPochhammer_eval_cast, ascPochhammer_nat_eq_descFactorial]
   induction' b with b
   · simp
   · simp_rw [add_succ, succ_sub_one]
@@ -47,7 +48,7 @@ theorem cast_descFactorial : (a.descFactorial b : S) = (pochhammer S b).eval (a
     · rw [tsub_add_cancel_of_le h]
 #align nat.cast_desc_factorial Nat.cast_descFactorial
 
-theorem cast_factorial : (a ! : S) = (pochhammer S a).eval 1 := by
+theorem cast_factorial : (a ! : S) = (ascPochhammer S a).eval 1 := by
   rw [← zero_ascFactorial, cast_ascFactorial, cast_zero, zero_add]
 #align nat.cast_factorial Nat.cast_factorial
 
@@ -63,9 +64,9 @@ theorem cast_descFactorial_two : (a.descFactorial 2 : S) = a * (a - 1) := by
   rw [cast_descFactorial]
   cases a
   · simp
-  · rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, pochhammer_succ_right, pochhammer_one,
-      Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add, Polynomial.eval_X, cast_one,
-      Polynomial.eval_one]
+  · rw [succ_sub_succ, tsub_zero, cast_succ, add_sub_cancel, ascPochhammer_succ_right,
+      ascPochhammer_one, Polynomial.X_mul, Polynomial.eval_mul_X, Polynomial.eval_add,
+      Polynomial.eval_X, cast_one, Polynomial.eval_one]
 #align nat.cast_desc_factorial_two Nat.cast_descFactorial_two
 
 end Ring

d50b12ae

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -22,7 +22,7 @@ to `↑a - 1`, the other factor is `0` anyway.
 
 open Nat
 
-variable (S : Type _)
+variable (S : Type*)
 
 namespace Nat

d50b12ae

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module data.nat.factorial.cast
-! leanprover-community/mathlib commit d50b12ae8e2bd910d08a94823976adae9825718b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Polynomial.Pochhammer
 
+#align_import data.nat.factorial.cast from "leanprover-community/mathlib"@"d50b12ae8e2bd910d08a94823976adae9825718b"
+
 /-!
 # Cast of factorials

d50b12ae

feat: port Data.Nat.Factorial.Cast (#2801)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>

2fb506f6

`data.nat.factorial.cast` ⟷ `Mathlib.Data.Nat.Factorial.Cast`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 396

data.nat.factorial.cast ⟷ Mathlib.Data.Nat.Factorial.Cast

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 396

`data.nat.factorial.cast` ⟷ `Mathlib.Data.Nat.Factorial.Cast`