Theorem: LO.FirstOrder.Arith.Model.Nuon.len_append (Arithmetization/OmegaOne/Nuon.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* 𝐈𝚫₀ + 𝛀₁
I L S i X : M
hi : i ≤ ‖I‖
hX : 0 < X
⊢ ‖append I L S i X‖ = ‖X * bexp (I # L) (i * ‖L‖) + S % bexp (I # L) (i * ‖L‖)‖
Tactic:
simp [append, add_comm]
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* 𝐈𝚫₀ + 𝛀₁
I L S i X : M
hi : i ≤ ‖I‖
hX : 0 < X
⊢ ‖X‖ + log (bexp (I # L) (i * ‖L‖)) = ‖X‖ + i * ‖L‖
Tactic:
simp [log_bexp (mul_len_lt_len_hash hi)]
State after:
no goals