Theorem: alternatingGroup.V4_card (Jordan/V4.lean)

State before:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
hα4 : Fintype.card α = 4
⊢ Fintype.card ↥(V4 α) = 4
Tactic:
obtain ⟨S : Sylow 2 (alternatingGroup α)⟩ := Sylow.nonempty (G := alternatingGroup α)
State after:
case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
hα4 : Fintype.card α = 4
S : Sylow 2 ↥(alternatingGroup α)
⊢ Fintype.card ↥(V4 α) = 4

State before:
case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
hα4 : Fintype.card α = 4
S : Sylow 2 ↥(alternatingGroup α)
⊢ Fintype.card ↥(V4 α) = 4
Tactic:
rw [V4_is_unique_sylow α hα4 S]
State after:
case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
hα4 : Fintype.card α = 4
S : Sylow 2 ↥(alternatingGroup α)
⊢ Fintype.card ↥↑S = 4

State before:
case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
hα4 : Fintype.card α = 4
S : Sylow 2 ↥(alternatingGroup α)
⊢ Fintype.card ↥↑S = 4
Tactic:
exact A4_sylow_card α hα4 S
State after:
no goals