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Proof step 35 from proof leninv-inf (previous step)

# nσ = ∞, nσ[m2] = nσ[m1] + 1, stutf(nσ), m1 < m2 → nσ[m2] = nσ[m1], n0 ≠ 0 → nσ[m] = n0 - 1 ∧ ¬(m < m0 → nσ[m0] = n0 - 1), ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0], ∀ n. ∃ m. nσ[m] = n ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 36:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]

Rule argument

spec: <toplevel> name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, m2, m1]

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (mon≤(nσ) ↔ true);%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = n + 1 → ¬ m ≤ n; (s)% ⊦ ⌜m⌝ < ∞; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m = m + n ↔ n = 0; (s) Used terms: nσ, m2, m1