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Proof step 7 from proof monls-notsmall (previous step)

nσ[0] = 0, ⌜n0 +1 + 1⌝ < # nσ, mon<(nσ), ∀ nσ. nσ[0] = 0 ∧ ⌜n0 + 1⌝ < # nσ ∧ mon<(nσ) → (n0 < nσ[n0 + 1] ↔ true) ⊦ n0 +1 < nσ[n0 +1 + 1] ↔ true

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
nσ[0] = 0, ⌜2⌝ + ⌜n0⌝ < # nσ, mon<(nσ), nσ[2 + n0] ≤ n0 + 1, ∀ nσ0. nσ0[0] = 0 ∧ ⌜n0⌝ + ⌜1⌝ < # nσ0 ∧ mon<(nσ0) → n0 < nσ0[n0 + 1] ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)