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Proof step 1 from proof size-to (conclusion)

¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ

Additional information

Used simplifier rules: to-fin: ⊦ ⌜x⌝ to n = ⌜x to n⌝ ;%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%length-to: ¬ # x < n ⊦ #(x to n) = n;%to-inf: ⊦ ⌜nf⌝ to n = ⌜nf to n⌝ ;%inf-size-to: ⊦ # ⌜nf to n⌝ = ⌜n⌝ ;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%inj: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; from specification nat-inf-basic%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat