Theorem: LO.FirstOrder.Arith.Model.two_mul_add_one_lt_two_mul_of_lt (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 : M
h : a < b
⊢ 2 * a + 1 < 2 * (a + 1)
Tactic:
simp [mul_add, one_lt_two]
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
h : a < b
⊢ 2 * (a + 1) ≤ 2 * b
Tactic:
simp [←lt_iff_succ_le, h]
State after:
no goals