Theorems · Theorem · geometry

AffineEquiv.ofBijective_apply

∀ {k : Type u_1} {P₁ : Type u_2} {P₂ : Type u_3} {V₁ : Type u_6} {V₂ : Type u_7} [inst : Ring k]
  [inst_1 : AddCommGroup V₁] [inst_2 : AddCommGroup V₂] [inst_3 : Module k V₁] [inst_4 : Module k V₂]
  [inst_5 : AddTorsor V₁ P₁] [inst_6 : AddTorsor V₂ P₂] {φ : P₁ →ᵃ[k] P₂} (hφ : Function.Bijective ⇑φ) (a : P₁),
  (AffineEquiv.ofBijective hφ) a = φ a

Defined in: Mathlib.LinearAlgebra.AffineSpace.AffineEquiv
Cited by: 0 results in Mathlib
Foundations: Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup AddCommGroup Module Module AddTorsor AddTorsor

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DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
AddTorsorstatement and proof · cited by 1,657
Function.Bijectivestatement and proof · cited by 863
AffineMapstatement and proof · cited by 674
AffineEquivstatement · cited by 191
AffineEquiv.ofBijectivestatement and proof · cited by 3

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