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Proof step 46 from proof embed-split (previous step)

mk(rs, f, g) = mk(rs0, f0, g0) ∪ Ha, a[P1](Ha), a[P0](mk(rs0, f0, g0)), mk(rs0, f0, g0) ⊥ Ha, ∃ rs, f, g. Ha = mk(rs, f, g) ⊦ a[P0 * P1](mk(rs, f, g))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
mk(rs, f, g) = mk(rs0, f0, g0) ∪ mk(rs1, f1, g1), rs0 ∩ rs1 = ∅, a[P0](mk(rs0, f0, g0)), a[P1](mk(rs1, f1, g1)) ⊦ a[P0 * P1](mk(rs, f, g))

Rule argument

Additional information

Used simplifier rules: ⊦ mk(rs0, f, g) ⊥ mk(rs1, f0, g0) ↔ rs0 ∩ rs1 = ∅; (s)