Theorem: LO.FirstOrder.Arith.Model.mod_mul_add_of_lt (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
a b r : M
hr : r < b
⊢ (a * b + r) % b = r
Tactic:
simp [mod_def, div_mul_add a b hr, mul_comm]
State after:
no goals