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Proof step 5 from proof mapex-put-rw (previous step)

((r => o * P))(H), r ∈ H ⊦ o0 = o1 ∧ ((r =>_ * P))(H) ↔ o0 = o1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
((r => o * P))(H) ⊦ ∃ o. ((r => o * P))(H)

Rule argument

Additional information

Used simplifier rules: mapex: ⊦ r =>_ = _∃(λ o. r => o);%ex3-shift: ⊦ ((_∃ oP * P))(H) ↔ (∃ o. ((oP(o) * P))(H));%map-in: ⊦ ((r => o * P))(H) → r ∈ H;%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep