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Proof step 54 from proof embed-split (previous step)

mk(rs, f, g) = mk(rs0, f0, g0) ∪ mk(rs1, f1, g1), rs0 ∩ rs1 = ∅, a[P1](mk(rs1, f1, g1)), a[P0](mk(rs0, f0, g0)) ⊦ mk(rs0, f0) ⊥ mk(rs1, f1) ∧ mk(rs, f) = mk(rs0, f0) ∪ mk(rs1, f1) ∧ P0(mk(rs0, f0)) ∧ P1(mk(rs1, f1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
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)) ⊦ mk(rs, f) = mk(rs0, f0) ∪ mk(rs1, f1) ∧ P0(mk(rs0, f0)) ∧ P1(mk(rs1, f1))

Rule argument

Additional information

Used simplifier rules: ⊦ mk(rs0, f0) ⊥ mk(rs1, f1) ↔ rs0 ∩ rs1 = ∅; (s)