Theorem: LO.FirstOrder.Arith.Model.add_sub_self (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
⊢ a + b - b = a
Tactic:
symm
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
⊢ a = a + b - b

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
⊢ a = a + b - b
Tactic:
simpa [add_comm b] using sub_spec_of_ge (@le_add_self _ _ b a)
State after:
no goals