case a
R : Type u_4
B : Type u_1
F : Type u_2
E : B → Type u_3
inst✝⁹ : Semiring R
inst✝⁸ : TopologicalSpace F
inst✝⁷ : TopologicalSpace B
inst✝⁶ : TopologicalSpace (TotalSpace E)
e✝ : Trivialization F TotalSpace.proj
x : TotalSpace E
b✝ : B
y : E b✝
inst✝⁵ : AddCommMonoid F
inst✝⁴ : Module R F
inst✝³ : (x : B) → AddCommMonoid (E x)
inst✝² : (x : B) → Module R (E x)
e e' : Trivialization F TotalSpace.proj
inst✝¹ : Trivialization.IsLinear R e
inst✝ : Trivialization.IsLinear R e'
b : B
hb : b ∈ e'.baseSet ∩ e.baseSet
⊢ (ContinuousLinearEquiv.symm (coordChangeL R e e' b)).toLinearEquiv = (coordChangeL R e' e b).toLinearEquiv
R : Type u_4
B : Type u_1
F : Type u_2
E : B → Type u_3
inst✝⁹ : Semiring R
inst✝⁸ : TopologicalSpace F
inst✝⁷ : TopologicalSpace B
inst✝⁶ : TopologicalSpace (TotalSpace E)
e✝ : Trivialization F TotalSpace.proj
x : TotalSpace E
b✝ : B
y : E b✝
inst✝⁵ : AddCommMonoid F
inst✝⁴ : Module R F
inst✝³ : (x : B) → AddCommMonoid (E x)
inst✝² : (x : B) → Module R (E x)
e e' : Trivialization F TotalSpace.proj
inst✝¹ : Trivialization.IsLinear R e
inst✝ : Trivialization.IsLinear R e'
b : B
hb : b ∈ e'.baseSet ∩ e.baseSet
⊢ ContinuousLinearEquiv.symm (coordChangeL R e e' b) = coordChangeL R e' e b
apply ContinuousLinearEquiv.toLinearEquiv_injective
no goals
case a
R : Type u_4
B : Type u_1
F : Type u_2
E : B → Type u_3
inst✝⁹ : Semiring R
inst✝⁸ : TopologicalSpace F
inst✝⁷ : TopologicalSpace B
inst✝⁶ : TopologicalSpace (TotalSpace E)
e✝ : Trivialization F TotalSpace.proj
x : TotalSpace E
b✝ : B
y : E b✝
inst✝⁵ : AddCommMonoid F
inst✝⁴ : Module R F
inst✝³ : (x : B) → AddCommMonoid (E x)
inst✝² : (x : B) → Module R (E x)
e e' : Trivialization F TotalSpace.proj
inst✝¹ : Trivialization.IsLinear R e
inst✝ : Trivialization.IsLinear R e'
b : B
hb : b ∈ e'.baseSet ∩ e.baseSet
⊢ (ContinuousLinearEquiv.symm (coordChangeL R e e' b)).toLinearEquiv = (coordChangeL R e' e b).toLinearEquiv
rw [coe_coordChangeL' e' e hb, (coordChangeL R e e' b).symm_toLinearEquiv,
  coe_coordChangeL' e e' hb.symm, LinearEquiv.trans_symm, LinearEquiv.symm_symm]