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Proof step 22 from proof embed-split (previous step)

rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0[rs1, f], P1[rs0, f], ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g)), a[P0](mk(rs1, f, g)) ∧ a[P1](mk(rs0, f, g)) ∧ mk(rs1, f, g) ⊥ mk(rs0, f, g)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P1[rs0, f], P0[rs1, f], ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g)), a[P0](mk(rs1, f, g)) ∧ a[P1](mk(rs0, f, g))

Rule argument

Additional information

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