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[Merged by Bors] - chore: forward-port leanprover-community/mathlib#19021 #4257

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8 changes: 7 additions & 1 deletion Mathlib/LinearAlgebra/Basis.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp

! This file was ported from Lean 3 source module linear_algebra.basis
! leanprover-community/mathlib commit 04cdee31e196e30f507e8e9eb2d06e02c9ff6310
! leanprover-community/mathlib commit 13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395

Check notice on line 7 in Mathlib/LinearAlgebra/Basis.lean

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Synchronization

See https://leanprover-community.github.io/mathlib-port-status/file/linear_algebra/basis?range=04cdee31e196e30f507e8e9eb2d06e02c9ff6310..13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -980,6 +980,12 @@
simp only [Finset.mem_univ, if_true, Pi.zero_apply, one_smul, Finset.sum_ite_eq', zero_smul]
#align basis.of_equiv_fun_equiv_fun Basis.ofEquivFun_equivFun

@[simp]
theorem Basis.equivFun_ofEquivFun (e : M ≃ₗ[R] ι → R) : (Basis.ofEquivFun e).equivFun = e := by
ext j
simp_rw [Basis.equivFun_apply, Basis.ofEquivFun_repr_apply]
#align basis.equiv_fun_of_equiv_fun Basis.equivFun_ofEquivFun

variable (S : Type _) [Semiring S] [Module S M']

variable [SMulCommClass R S M']
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7 changes: 6 additions & 1 deletion Mathlib/LinearAlgebra/StdBasis.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@
Authors: Johannes Hölzl

! This file was ported from Lean 3 source module linear_algebra.std_basis
! leanprover-community/mathlib commit f8c79b0a623404854a2902b836eac32156fd7712
! leanprover-community/mathlib commit 13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395

Check notice on line 7 in Mathlib/LinearAlgebra/StdBasis.lean

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Synchronization

See https://leanprover-community.github.io/mathlib-port-status/file/linear_algebra/std_basis?range=f8c79b0a623404854a2902b836eac32156fd7712..13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -289,6 +289,11 @@
theorem basisFun_repr (x : η → R) (i : η) : (Pi.basisFun R η).repr x i = x i := by simp [basisFun]
#align pi.basis_fun_repr Pi.basisFun_repr

@[simp]
theorem basisFun_equivFun : (Pi.basisFun R η).equivFun = LinearEquiv.refl _ _ :=
Basis.equivFun_ofEquivFun _
#align pi.basis_fun_equiv_fun Pi.basisFun_equivFun

end

end Module
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