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Proof step 4 from proof lift-unknown (previous step)

(_∃(λ o, a. r ==>(o, a)) * R)[rs, f, g] ⊦ ∃ a. (a[r =>_] * R)[rs, f, g]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
(r ==>(o, a) * R)[rs, f, g] ⊦ ∃ a. (a[r =>_] * R)[rs, f, g]

Rule argument

Additional information

Used simplifier rules: sep-com: ⊦ R0 * R1 = R1 * R0; from specification heap-sep[heap-aux]%sep-ass: ⊦ (R0 * R1) * R2 = R0 * R1 * R2; from specification heap-sep[heap-aux]% ⊦ (_∃ oR * R)[rs, f, g] ↔ (∃ o, a. (oR(o, a) * R)[rs, f, g]); (s)