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Proof step 11 from proof sep-forall-reduce-true (previous step)

((nP ⊗_(n, m0) * nP(n + m0) * P0))(zh), ¬ m0 < m0 ∧ ((nP(n + m0) * P0 * nP ⊗_(n, m0)))(zh) → ((nP2(n + m0) * true * P0 * nP ⊗_(n, m0)))(zh), ∀ n0, P. ¬ m0 < n0 ∧ ((nP(n + n0) * P))(zh) → ((nP2(n + n0) * true * P))(zh), ∀ nP, n, P0, zh, nP2. ((nP ⊗_(n, m0) * P0))(zh) ∧ (∀ n0, P. n0 < m0 ∧ ((nP(n + n0) * P))(zh) → ((nP2(n + n0) * true * P))(zh)) → ((nP2 ⊗_(n, m0) * true * P0))(zh) ⊦ ((nP2 ⊗_(n, m0) * nP2(n + m0) * true * P0))(zh)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
((nP ⊗_(n, m0) * nP(n + m0) * P0))(zh), ((nP2(n + m0) * true * P0 * nP ⊗_(n, m0)))(zh), ∀ nP, n, P0, zh, nP2. ((nP ⊗_(n, m0) * P0))(zh) ∧ (∀ n0, P. n0 < m0 ∧ ((nP(n + n0) * P))(zh) → ((nP2(n + n0) * true * P))(zh)) → ((nP2 ⊗_(n, m0) * true * P0))(zh), ∀ n0, P. ¬ m0 < n0 ∧ ((nP(n + n0) * P))(zh) → ((nP2(n + n0) * true * P))(zh) ⊦ ((nP2 ⊗_(n, m0) * nP2(n + m0) * true * P0))(zh)

Rule argument

Additional information

Used simplifier rules: sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]% ⊦ ¬ n < n; (s)