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Proof step 19 from proof stutf-maxinf-is-fin (previous step)

nσ[n1] = nσ[m0], # nσ = ∞, m0 < n1, n0 < n1, nσ[m0] < nσ[n0], m0 ≤ n, nσ[m0] ≤ nσ[n], stutf(nσ), m0 ≤ n0 ⊦ n1 = 0, nσ[n0] = 0, nσ[n0] = nσ[m0]

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, n0, n1] flags: current, []

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%lels-03: ⊦ m < n → m ≤ n; from specification nat%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: nσ, n0, n1