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Proof step 35 from proof embed-split (previous step)

rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0(mk(rs1, f)), P1(mk(rs0, f)), r ∈ rs1, ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ # rs1 = 0, g(r) = a, rs1 = ∅, ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g))

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: r

Additional information

Used simplifier rules: ⊦ r ∈ rs ∪ rs0 ↔ ¬(¬ r ∈ rs ∧ ¬ r ∈ rs0); (ss)%una: ⊦ (rs ∪ rs0) ∪ rs1 = rs ∪ rs0 ∪ rs1; from specification set-union[refset]%unc: ⊦ rs ∪ rs0 = rs0 ∪ rs; from specification set-union[refset] Used terms: r