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Proof step 12 from proof monls-exists-maxleq (previous step)

n < nσ[m], nσ[0] < nσ[m], ⌜m⌝ < # nσ, nσ[0] < n, nσ[0] + 1 < nσ[m], mon<(nσ) ⊦ n = nσ[m], ∃ m0. nσ[m0] < n ∧ n ≤ nσ[m0 + 1] ∧ m0 ≤ m

User applied rule insert lemma

And obtained the following new goals

Proof step 13:
mon<(nσ), nσ[0] ≤ n, n < nσ[m], ⌜m⌝ < # nσ ⊦ ∃ m0. nσ[m0] ≤ n ∧ n < nσ[m0 + 1] ∧ m0 ≤ m
Proof step 14:
nσ[0] + 1 < nσ[m], nσ[0] < n, ⌜m⌝ < # nσ, nσ[0] < nσ[m], n < nσ[m], mon<(nσ), ∃ m0. nσ[m0] ≤ n ∧ n < nσ[m0 + 1] ∧ m0 ≤ m ⊦ n = nσ[m], ∃ m0. nσ[m0] < n ∧ n ≤ nσ[m0 + 1] ∧ m0 ≤ m

Rule argument

spec: <toplevel> name: monls-exists-maxls seq: mon<(nσ), nσ[0] ≤ n, n < nσ[m], ⌜m⌝ < # nσ ⊦ ∃ m0. nσ[m0] ≤ n ∧ n < nσ[m0 + 1] ∧ m0 ≤ m subst: [nσ, n, m] → [nσ, n, m]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → ¬ n < m; (s) Used terms: nσ, n, m