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Proof step 6 from proof lift-prop (previous step)

⊦ ((a[⌜bv⌝ ] ∧ emp))(mk(rs, f, g)) ↔ (⌜bv⌝ ∧ emp)[rs, f, g]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ a[⌜bv⌝ ](mk(rs, f, g)) ∧ mk(rs, f, g) = ∅ ↔ (⌜bv⌝ ∧ emp)[rs, f, g]

Rule argument

Additional information

Used simplifier rules: and-com: ⊦ (R0 ∧ R1) = (R1 ∧ R0); from specification heap-sep[heap-aux]%and-ass: ⊦ ((R0 ∧ R1) ∧ R2) = (R0 ∧ R1 ∧ R2); from specification heap-sep[heap-aux]% ⊦ emp(Ha) ↔ Ha = ∅; (s)% ⊦ ((R0 ∧ R1))(Ha) ↔ R0(Ha) ∧ R1(Ha); (s)