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Proof step 12 from proof sep-forall-reduce (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 13:
((nP2(n + m0) * P0 * nP ⊗_(n, m0)))(zh), ((nP ⊗_(n, m0) * nP(n + m0) * P0))(zh), ((nP ⊗_(n, m0) * P0 * nP2(n + m0)))(zh) ∧ (∀ n0, P. n0 < m0 ∧ ((nP(n + n0) * P))(zh) → ((nP2(n + n0) * P))(zh)) → ((nP2 ⊗_(n, m0) * P0 * nP2(n + m0)))(zh), ∀ n0, P. ¬ m0 < n0 ∧ ((nP(n + n0) * P))(zh) → ((nP2(n + n0) * P))(zh) ⊦ ((nP2 ⊗_(n, m0) * nP2(n + m0) * P0))(zh)

Rule argument

pos: left 3 terms: nP, n, P0 * nP2(n + m0), zh, nP2 abort: F discard: T computed: T

Additional information

Used terms: nP, n, P0 * nP2(n + m0), zh, nP2