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Proof step 2 from proof sep-forall-reduce-true (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 3:
((nP ⊗_(n, m0 +1) * P0))(zh), ∀ n0, P. n0 < m0 +1 ∧ ((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 +1) * true * P0))(zh)

Rule argument

indvar: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ nP0 ⊗_(n, 0) = emp; (s)% ⊦ emp * P0 = P0; (s)%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]% ⊦ P0(zh) → ((true * P0))(zh); (s)