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Proof step 131 from proof inv-get-inverse-between (previous step)

mon≤(nσ) ∧ m1 ≤ n1 ∧ ⌜n1⌝ < # nσ → nσ[m1] ≤ nσ[n1], # nσ = ∞, nσ[n] = nσ[n1] + 1, n1 + m + 1 < m1, n ≤ m1, stutf(nσ), nσ[n1] < nσ[m1], n1 + m + 1 < n, nσ[n] ≤ nσ[m1], ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1, ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m. nσ[m] = nσ[n] → ¬ n < m ⊦ nσ[n] = nσ[m1] + 1, nσ[m1] = 0, nσ[n1 + m + 1] = nσ[n], n = 0, m1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 132:
nσ[n] = nσ[n1] + 1, # nσ = ∞, nσ[n] ≤ nσ[m1], n1 + m + 1 < n, nσ[n1] < nσ[m1], stutf(nσ), n ≤ m1, n1 + m + 1 < m1, n1 < m1, ∀ m. nσ[m] = nσ[n] → ¬ n < m, ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1 ⊦ m1 = 0, n = 0, nσ[n1 + m + 1] = nσ[n], nσ[m1] = 0, nσ[n] = nσ[m1] + 1

Rule argument

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat