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Proof step 9 from proof prop-emp (conclusion)

⊦ ((⌜bv⌝ ∧ emp) * P)(H) ↔ ¬ ¬ (bv ∧ P(H))

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : prop-shift, , , ⊦ (⌜bv⌝ ∧ P0) * P1 = (⌜bv⌝ ∧ P0 * P1)], [CSIMPNAMEDSEQ : emp-sep, , , ⊦ emp * P = P], [CSIMPNAMEDSEQ : sep-ass, , , ⊦ (P0 * P1) * P2 = P0 * P1 * P2], [CSIMPNAMEDSEQ : sep-com, , , ⊦ P0 * P1 = P1 * P0], [CSIMPNAMEDSEQ : and-ass, , , ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2)], [CSIMPNAMEDSEQ : and-com, , , ⊦ (P0 ∧ P1) = (P1 ∧ P0)], [CSIMPNAMEDSEQ : and, , , ⊦ (P0 ∧ P1)(H) ↔ ¬ ¬ (P0(H) ∧ P1(H))], [CSIMPNAMEDSEQ : prop, , , ⊦ ⌜bv⌝ (H) ↔ bv])]]