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Proof step 3 from proof extensionality (previous step)

# ⌜x⌝ = # σ1, ∀ n. ⌜n⌝ < # σ1 → ⌜x⌝ [n] = σ1[n] ⊦ ⌜x⌝ = σ1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⌜# x⌝ = # σ1, ∀ n. n < # x → x[n] = σ1[n] ⊦ ⌜x⌝ = σ1

Rule argument

Additional information

Used simplifier rules: size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%sel-fin: ⊦ ⌜x⌝ [n] = x[n];%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf