Theorem: LO.FirstOrder.Arith.Model.mod_mul_add (Arithmetization/Basic/IOpen.lean)

State before:
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : M ⊧ₘ* 𝐏𝐀⁻
inst✝ : M ⊧ₘ* 𝐈open
b a c : M
pos : 0 < b
⊢ (a * b + c) % b = c % b
Tactic:
simp [mod_def, div_mul_add_self, pos, mul_add, ←sub_sub, show b * a = a * b from mul_comm _ _]
State after:
no goals