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Proof step 1 from proof get-cons-succ (conclusion)

⊦ (⌜a '⌝ + σ)[n + 1] = σ[n]

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ (⌜a '⌝ + ⌜nf⌝ )[n + 1] = ⌜nf⌝ [n]

Rule argument

indvar: σ

Additional information

Used simplifier rules: get-append2-fin: ⊦ (⌜x⌝ + ⌜x0⌝ )[m] = (x + x0)[m];%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%sel-fin: ⊦ ⌜x⌝ [n] = x[n];%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%get-succ: ⊦ (a ' + x)[n + 1] = x[n]; from specification list-del%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