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Proof step 3 from proof to-empty-fin2 (previous step)

x to n = [], n ≤ # x ⊦ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n])

Rule argument

spec: list-del name: extension seq: ⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n]) subst: [y, x] → [[], x to n] flags: <all paths>

Additional information

Used simplifier rules: length-to: ¬ # x < n ⊦ #(x to n) = n;% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ # [] = 0; (s) Used terms: [], x to n