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Proof step 8 from proof mininv-inverts-inner-succ (previous step)

# nσ = ⌜n0⌝ , min(nσ, nσ[n] + 1) = n0, ⌜n⌝ < # nσ, mon<(nσ), nσ[n0 - 1] ≤ nσ[n] ⊦ n0 = n + 1, nσ = [], # nσ = ∞

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# nσ = ⌜min(nσ, nσ[n] + 1)⌝ , nσ[min(nσ, nσ[n] + 1) - 1] ≤ nσ[n], mon<(nσ), n < min(nσ, nσ[n] + 1), n + 1 < min(nσ, nσ[n] + 1) ⊦ nσ = [], min(nσ, nσ[n] + 1) = n + 1, min(nσ, nσ[n] + 1) = 0

Rule argument

Additional information

Used simplifier rules: succ-03: ⊦ m < n ∧ m + 1 ≠ n → m + 1 < n; (forward) from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic