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Proof step 63 from proof eq-leninv (previous step)

nσ[m0 + 1] = nσ[n], nσ[m0] + 1 = nσ[n], # nσ = ∞, m0 < m, nσ[m0] < nσ[n], stutf(nσ), nσ[n] < nσ[m], nσ[m0] < nσ[m], m ≤ n, m0 < n, ∀ m0. n < m0 → nσ[m0] = nσ[n] ⊦ m = 0, nσ[m] = nσ[n], n = 0, nσ[n] = 0, nσ[m] = 0

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, m, n] flags: current, []

Additional information

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