Theorem: LO.FirstOrder.Arith.Model.le_mul_self_of_pos_left (Arithmetization/Basic/PeanoMinus.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 : M
hy : 0 < b
⊢ a ≤ b * a
Tactic:
have : 1 * a ≤ b * a := mul_le_mul_of_nonneg_right (one_le_of_zero_lt b hy) (by simp)
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 : M
hy : 0 < b
this : 1 * a ≤ b * a
⊢ a ≤ b * a

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 : M
hy : 0 < b
this : 1 * a ≤ b * a
⊢ a ≤ b * a
Tactic:
simpa using this
State after:
no goals

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 : M
hy : 0 < b
⊢ 0 ≤ a
Tactic:
simp
State after:
no goals