Theorem: LO.FirstOrder.Arith.Model.two_mul_lt_sq (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 i : M
h : 2 < i
⊢ 2 * i < i ^ 2
Tactic:
simp [sq]
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 i : M
h : 2 < i
⊢ 2 * i < i * i

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 i : M
h : 2 < i
⊢ 2 * i < i * i
Tactic:
exact (mul_lt_mul_right (show 0 < i from pos_of_gt h)).mpr h
State after:
no goals