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Proof step 5 from proof extensionality (previous step)

⌜# x⌝ = # ⌜x0⌝ , ∀ n. n < # x → x[n] = ⌜x0⌝ [n] ⊦ ⌜x⌝ = ⌜x0⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# x = # x0, ∀ n. n < # x0 → x[n] = x0[n] ⊦ x = x0

Rule argument

Additional information

Used simplifier rules: size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%sel-fin: ⊦ ⌜x⌝ [n] = x[n];% ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; (s)% ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s)