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Proof step 3 from proof ton-fromn (previous step)

σ = ⌜x⌝ ⊦ (σ to n) from n = [], # σ < ⌜n⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n ≤ # x ⊦ (x to n) from n = []

Rule argument

Additional information

Used simplifier rules: to-fin: ⊦ ⌜x⌝ to n = ⌜x to n⌝ ;%from-fin: ⊦ ⌜x⌝ from n = ⌜x from n⌝ ;%fin-empty: ⊦ ⌜x⌝ = [] ↔ x = [];%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf