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Proof step 13 from proof Sep-forall-prove-imp (previous step)

n0 < m0, nP0(n) ⊆ nP1(n), ∀ n0. ¬ m0 < n0 → nP0(n + n0) ⊆ nP1(n + n0) ⊦ nP0((n + 1) + n0) ⊆ nP1((n + 1) + n0), nP0 ⊗_(n + 1, m0) ⊆ nP1 ⊗_(n + 1, m0), nP0(n) * nP0 ⊗_(n + 1, m0) ⊆ nP1(n) * nP1 ⊗_(n + 1, m0)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: n0 + 1

Additional information

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