Theorem: LO.FirstOrder.Arith.Model.Nuon.ext_append_last (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 : ‖X‖ ≤ ‖L‖
⊢ append I L S i X{L}[i] = (S % bexp (I # L) (i * ‖L‖) + X * bexp (I # L) (i * ‖L‖)){L}[i + 0]
Tactic:
simp [append]
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 : ‖X‖ ≤ ‖L‖
⊢ i + 0 ≤ ‖I‖
Tactic:
simpa using hi
State after:
no goals