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Proof step 1 from proof mapex-put (conclusion)

r ∈ H ⊦ ((r =>_ * P))(H[r, o]) ↔ ((r => o * P))(H[r, o])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
r ∈ H ⊦ (∃ o0. ((r => o0 * P))(H[r, o])) ↔ ((r => o * P))(H[r, o])

Rule argument

Additional information

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