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Proof step 6 from proof split-uni (conclusion)

⊦ P0[rs0, f] ∧ P1[rs1, f] ∧ rs0 ∩ rs1 = ∅ → (¬ (P0 * P1)[rs0 ∪ rs1, f] ↔ false)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : apply, , , ⊦ P[rs, f] ↔ P(mk(rs, f))], [CSIMPNAMEDSEQ : uni, , , ⊦ rs0 ∩ rs1 = ∅ → mk(rs0 ∪ rs1, f) = mk(rs0, f) ∪ mk(rs1, f)], [CSIMPSEQ : ⊦ rs ∪ rs0 = rs0 ∪ rs], [CSIMPSEQ : ⊦ (rs ∪ rs0) ∪ rs1 = rs ∪ rs0 ∪ rs1], [CSIMPSEQ : ⊦ rs ∩ rs0 = rs0 ∩ rs], [CSIMPSEQ : ⊦ (rs ∩ rs0) ∩ rs1 = rs ∩ rs0 ∩ rs1])]]