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Proof step 4 from proof toone-equal (previous step)

⊦ ⌜x⌝ to 1 = ⌜a '⌝ ↔ ⌜x⌝ [0] = a, ⌜x⌝ = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ x to 1 = a ' ↔ x.head = a, x = []

Rule argument

Additional information

Used simplifier rules: fin-empty: ⊦ ⌜x⌝ = [] ↔ x = [];%to-fin: ⊦ ⌜x⌝ to n = ⌜x to n⌝ ;%sel-fin: ⊦ ⌜x⌝ [n] = x[n];% ⊦ x ≠ [] → x[0] = x.head; (s)% ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; (s)