Theorem: LO.FirstOrder.Arith.Model.LenBit.add_self (Arithmetization/ISigmaZero/Exponential/Pow2.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* 𝐈open
i a : M
h : a < i
⊢ LenBit i (a + i)
Tactic:
have pos : 0 < i := by exact pos_of_gt h
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* 𝐈open
i a : M
h : a < i
pos : 0 < i
⊢ LenBit i (a + i)

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* 𝐈open
i a : M
h : a < i
pos : 0 < i
⊢ LenBit i (a + i)
Tactic:
simp [LenBit.iff_rem, div_add_self_right _ pos, h, 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* 𝐈open
i a : M
h : a < i
⊢ 0 < i
Tactic:
exact pos_of_gt h
State after:
no goals