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Proof step 58 from proof eq-leninv (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 59:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]
Proof step 60:
mon≤(nσ) ∧ m0 + 1 ≤ m ∧ ⌜m⌝ < # nσ → nσ[m0 + 1] ≤ nσ[m], # nσ = ∞, nσ[m0] + 1 = nσ[n], nσ[m0 + 1] = nσ[n], stutf(nσ), m0 < n, nσ[m0] < nσ[n], m0 < m, ∀ m0. n < m0 → nσ[m0] = nσ[n] ⊦ nσ[n] = 0, n = 0, nσ[m] = nσ[n], m = 0

Rule argument

spec: inst: name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, m0 + 1, m] flags: current, []

Additional information

Used terms: nσ, m0 + 1, m