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Proof step 2 from proof to-succ-cons (previous step)

⊦ ⌜a '⌝ + σ to n + 1 = ⌜a '⌝ + (σ to n)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
⊦ ⌜a '⌝ + ⌜nf⌝ to n + 1 = ⌜a '⌝ + (⌜nf⌝ to n)

Rule argument

indvar: σ

Additional information

Used simplifier rules: to-appfin: ⊦ ⌜x⌝ + ⌜y⌝ to n = ⌜x + y to n⌝ ;%to-succ-cons-l-lem: ⊦ a ' + x to n + 1 = a + (x to n);%append-finfin: ⊦ ⌜x + y⌝ = ⌜x⌝ + ⌜y⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%to-fin: ⊦ ⌜x⌝ to n = ⌜x to n⌝ ;%eq-stream-to-list-2-2: ⊦ ⌜x⌝ + ⌜y⌝ = ⌜x0⌝ + ⌜z⌝ ↔ x + y = x0 + z;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list