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Proof step 3 from proof monle-leq (previous step)

nσ[n] < nσ[m], ⌜n⌝ < # nσ, mon≤(nσ), m ≤ n ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 4:
m1 +1 = n - m, ⌜n⌝ < # nσ, nσ[n] < nσ[m], mon≤(nσ), m ≤ n, ∀ n, m, nσ. ¬(m1 = n - m ∧ nσ[n] < nσ[m] ∧ ⌜n⌝ < # nσ ∧ mon≤(nσ) ∧ m ≤ n) ⊦

Rule argument

term: n - m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ m ≤ n → (n - m = 0 ↔ n = m); (s)% ⊦ ¬ n < n; (s)