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Proof step 27 from proof maxinf-skolemf (previous step)

n3 + n0 - 1 < n, np(n), np(n0), ∀ n1, n2, np. n1 - n2 < n3 → np(n2) → (∃ n. np(n) ∧ (∀ n0. n < n0 → ¬ np(n0))) ∨ (∃ n0. n1 < n0 ∧ np(n0)) ⊦ np(n3 + n0), ∃ n1. n3 + n0 < n1 ∧ np(n1), ∃ n. np(n) ∧ (∀ n0. n < n0 → ¬ np(n0))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
n3 + n0 = m + 1, m < n, np(n0), np(n), ∀ n1, n2, np. n1 - n2 < n3 → np(n2) → (∃ n. np(n) ∧ (∀ n0. n < n0 → ¬ np(n0))) ∨ (∃ n0. n1 < n0 ∧ np(n0)) ⊦ n3 + n0 = 0, np(n3 + n0), ∃ n. np(n) ∧ (∀ n0. n < n0 → ¬ np(n0)), ∃ n1. n3 + n0 < n1 ∧ np(n1)

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n3 + n0, m]

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n3 + n0, m