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Proof step 51 from proof inv-get-inverse-last (previous step)

nσ[m1] = nσ[n1], # nσ = ∞, stutf(nσ), n1 ≤ m1, ∀ m0. m1 < m0 → nσ[m0] = nσ[n1] + 1, ∀ m0. nσ[m0] = nσ[n1] → ¬ n1 < m0 ⊦ nσ[n1 + m + 1] = nσ[n1] + 1

User applied rule insert lemma

And obtained the following new goals

Proof step 52:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]
Proof step 53:
mon≤(nσ) ∧ n1 ≤ m1 ∧ ⌜m1⌝ < # nσ → nσ[n1] ≤ nσ[m1], nσ[m1] = nσ[n1], # nσ = ∞, stutf(nσ), n1 ≤ m1, ∀ m0. m1 < m0 → nσ[m0] = nσ[n1] + 1, ∀ m0. nσ[m0] = nσ[n1] → ¬ n1 < m0 ⊦ nσ[n1 + m + 1] = nσ[n1] + 1

Rule argument

spec: inst: name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, n1, m1] flags: current, []

Additional information

Used terms: nσ, n1, m1