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Proof step 21 from proof propagate (previous step)

H0 ∪ H3 ∪ H4 = H3 ∪ H2, !(me, O2, P)(H0), !(id, O2, P1)(H3), P0(H), rely(me, O1, H0 ∪ H, O2, H3 ∪ H2), H4 ⊥ H3, H3 ∪ H4 ⊥ H0, H0 ⊥ H, H3 ⊥ H2 ⊦ id = me, ((!(id, O2, P1) * true))(H3 ∪ H4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1)

Rule argument

spec: heap-sep name: split-union seq: ⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1) subst: [H1, H0, P1, P0] → [H4, H3, true, !(id, O2, P1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ true(H); (s)% ⊦ H0 ⊥ H1 → H1 ⊥ H0; (s) Used terms: H4, H3, true, !(id, O2, P1)