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Proof step 2 from proof lslen-fromnotempty (previous step)
| σ from n = [], ⌜n⌝ < # σ ⊦ |
Heuristic structural induction applied rule structural induction
And closed the goal!
Rule argument
term: σAdditional information
Used simplifier rules:
from-fin: ⊦ ⌜x⌝ from n = ⌜x from n⌝ ;%fin-empty: ⊦ ⌜x⌝ = [] ↔ x = [];%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%lslen-fromnotempty-list: ⊦ n < # x → (x from n = [] ↔ false);%from-inf: ⊦ ⌜nf⌝ from n = ⌜nf from n⌝ ;%fun-nonempty: ⊦ [] ≠ ⌜nf⌝ ;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf