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Proof step 8 from proof mininv-inverts-weak (previous step)

min(nσ, n) = (# nσ).n, ⌜min(nσ, n)⌝ < # nσ, nσ[min(nσ, n)] < n, nσ[min(nσ, n) - 1] < n, mon<(nσ) ⊦ # nσ = ∞, nσ = []

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat-inf name: elim seq: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ) subst: [n∞, m] → [# nσ, m]

Additional information

Used simplifier rules: ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ ¬ n < n; (s)% ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ); (elim) Used terms: # nσ, m