Theorem: LO.FirstOrder.Arith.Model.pow_four (Arithmetization/Vorspiel/Lemmata.lean)

State before:
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐏𝐀⁻
a b c x : M
⊢ x ^ 4 = x * x * x * x
Tactic:
rw [← three_add_one_eq_four, pow_add, pow_three]
State after:
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐏𝐀⁻
a b c x : M
⊢ x * x * x * x ^ 1 = x * x * x * x

State before:
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐏𝐀⁻
a b c x : M
⊢ x * x * x * x ^ 1 = x * x * x * x
Tactic:
simp
State after:
no goals