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Proof step 3 from proof get-append-notls (previous step)

⊦ (⌜x⌝ + σ1)[m] = σ1[m - (# ⌜x⌝ ).n], ⌜m⌝ < # ⌜x⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
# x ≤ m ⊦ (⌜x⌝ + σ1)[m] = σ1[m - # x]

Rule argument

Additional information

Used simplifier rules: size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%sel: ⊦ ⌜m⌝ .n = m; from specification nat-inf-basic