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Proof step 52 from proof inv-inverts-leq (previous step)

# nσ = ∞, nσ[n0] = nσ[n], nσ[n1] = nσ[n], ∞.n < n, nσ[n] ≤ nσ[m], stutf(nσ), m + 1 < n0, m + 1 < n1, m < n0, nσ[m + 1] ≤ nσ[n], nσ[m + 1] ≤ nσ[m], ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1 ⊦

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 12 terms: m +1

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%eq: ⊦ m = n + 1 → ¬ m ≤ n; from specification nat Used terms: m +1