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Proof step 2 from proof prop-emp (conclusion)

⊦ ((⌜bv⌝ ∧ emp) * P)[rs, f] ↔ ¬ ¬ (bv ∧ P[rs, f])

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : apply, , , ⊦ P[rs, f] ↔ P(mk(rs, f))], [CSIMPSEQ : ⊦ (true ∧ P) = P], [CSIMPSEQ : ⊦ ⌜true⌝ = true], [CSIMPSEQ : ⊦ ⌜bv⌝ (H) ↔ bv], [CSIMPSEQ : ⊦ (P0 ∧ P1)(H) ↔ ¬ ¬ (P0(H) ∧ P1(H))], [CSIMPSEQ : ⊦ (P0 ∧ P1) = (P1 ∧ P0)], [CSIMPSEQ : ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2)], [CSIMPSEQ : ⊦ P0 * P1 = P1 * P0], [CSIMPSEQ : ⊦ (P0 * P1) * P2 = P0 * P1 * P2], [CSIMPSEQ : ⊦ emp * P = P], [CSIMPSEQ : ⊦ (⌜bv⌝ ∧ P0) * P1 = (⌜bv⌝ ∧ P0 * P1)])]]