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Proof step 1 from proof append-from-gr-02 (conclusion)

⊦ # σ0 < ⌜m⌝ → σ0 + σ from m = σ from (m - (# σ0).n)

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ0

Additional information

Used simplifier rules: size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%append-from-gr-01: ⊦ # x < m → ⌜x⌝ + σ from m = σ from (m - # x);%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%append-inf: ⊦ ⌜nf⌝ + σ = ⌜nf⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%from-inf: ⊦ ⌜nf⌝ from n = ⌜nf from n⌝ ;%size-inf: ⊦ # ⌜nf⌝ = ∞;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%less-inf1: ⊦ ¬ ∞ < n∞; from specification nat-inf%sel: ⊦ ⌜m⌝ .n = m; from specification nat-inf-basic%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf