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Proof step 1 from proof to-attach (conclusion)

⊦ ⌜x + a '⌝ to # x = ⌜x⌝

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: x

Additional information

Used simplifier rules: to-fin: ⊦ ⌜x⌝ to n = ⌜x to n⌝ ;%to-zero-l: ⊦ x to 0 = [];%empty: ⊦ ⌜[]⌝ = [];%append-finfin: ⊦ ⌜x + y⌝ = ⌜x⌝ + ⌜y⌝ ;%to-succ-cons: ⊦ ⌜a '⌝ + σ to n + 1 = a + (σ to n);%append-to-size-01: ⊦ ⌜x⌝ + σ to # x = ⌜x⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%cons-append: ⊦ a + σ = ⌜a '⌝ + σ;%append-cancel-l: ⊦ ⌜x⌝ + σ0 = ⌜x⌝ + σ1 ↔ σ0 = σ1;%list freely generated by [], +;;% ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ [] + x = x; (s)% ⊦ # [] = 0; (s)