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Proof step 2 from proof monle-leq (previous step)

mon≤(nσ), m ≤ n, ⌜n⌝ < # nσ, nσ[n] < nσ[m] ⊦ nσ[m] = 0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ n, m, nσ. m1 = n - m ∧ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ ∧ nσ[n] < nσ[m] → nσ[m] = 0, m1 +1 = n - m, mon≤(nσ), m ≤ n, ⌜n⌝ < # nσ, nσ[n] < nσ[m] ⊦ nσ[m] = 0

Rule argument

term: n - m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;%zero-02: ⊦ m ≤ n → (n - m = 0 ↔ n = m); from specification nat%ref-1: ⊦ ¬ n < n; from specification nat-basic1