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Proof step 1 from proof toone-cons (conclusion)

⊦ ⌜a '⌝ + σ to 1 = ⌜a '⌝

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ

Additional information

Used simplifier rules: to-appfin: ⊦ ⌜x⌝ + ⌜y⌝ to n = ⌜x + y to n⌝ ;%toone-cons-fin: ⊦ a ' + y to 1 = a ';%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%append-empty-01: ⊦ σ0 + σ1 = [] ↔ σ0 = [] ∧ σ1 = [];%fin-empty: ⊦ ⌜x⌝ = [] ↔ x = [];%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%toone-equal: σ ≠ [] ⊦ σ to 1 = ⌜a '⌝ ↔ σ[0] = a;%get-cons-zero: ⊦ (⌜a '⌝ + σ)[0] = a;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%e: ⊦ a ' ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic