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Proof step 36 from proof propagate (previous step)

(H0 ∪ H1)[r] = H3[r], !(id, O2, P1)(H3), !(me, O2, P)(H0), P0(H), rely(me, O1, H0 ∪ H, O2, H3 ∪ H2), r ∈ H3, r ∈ H0 ∪ H1, H3 ⊥ H2, H0 ⊥ H, H1 ⊥ H0 ⊦ id = me, r ∈ H0, r ∈ H1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1)

Rule argument

spec: heap name: in-uni seq: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1) subst: [H1, H0, r] → [H1, H0, r] flags: <all paths>

Additional information

Used simplifier rules: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1); (s)%r ∈ H0 ∪ H1 ⊦ H0 ⊥ H1 → (H0 ∪ H1)[r] = (r ∈ H0 ⊃ H0[r];H1[r]); (s)% ⊦ H0 ⊥ H1 → H1 ⊥ H0; (s) Used terms: H1, H0, r