Theorem: OnCycleFactors.θAux_apply_of_mem_fixedPoints_mem (Jordan/ConjClassCount.lean)

State before:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ θAux g k v x ∈ Function.fixedPoints ⇑g
Tactic:
rw [θAux_apply_of_mem_fixedPoints hx, Equiv.Perm.ofSubtype_apply_of_mem k hx]
State after:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑(k { val := x, property := hx }) ∈ Function.fixedPoints ⇑g

State before:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑(k { val := x, property := hx }) ∈ Function.fixedPoints ⇑g
Tactic:
exact (k _).prop
State after:
no goals