Theorems · Theorem · geometry

LinearIsometryEquiv.ofLinearIsometry.congr_simp

∀ {R : Type u_1} {R₂ : Type u_2} {E : Type u_5} {E₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [inst_2 : RingHomInvPair σ₁₂ σ₂₁] [inst_3 : RingHomInvPair σ₂₁ σ₁₂]
  [inst_4 : SeminormedAddCommGroup E] [inst_5 : SeminormedAddCommGroup E₂] [inst_6 : Module R E] [inst_7 : Module R₂ E₂]
  (f f_1 : E →ₛₗᵢ[σ₁₂] E₂) (e_f : f = f_1) (g g_1 : E₂ →ₛₗ[σ₂₁] E) (e_g : g = g_1)
  (h₁ : f.toLinearMap ∘ₛₗ g = LinearMap.id) (h₂ : g ∘ₛₗ f.toLinearMap = LinearMap.id),
  LinearIsometryEquiv.ofLinearIsometry f g h₁ h₂ = LinearIsometryEquiv.ofLinearIsometry f_1 g_1 ⋯ ⋯

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation

Cited by

3 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairSeminormedAddCommGroupSeminormedAddCommGroupModuleModule