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Proof step 21 from proof merge-owned (previous step)

rs2 ∩ rs = ∅, rs1 ∩ rs0 = ∅, rs2 ∪ rs = rs1 ∪ rs0, a0[P0][rs2, f, g], R0[rs, f, g], a[P][rs1, f, g], R[rs0, f, g] ⊦ a0 = a, (a[P] * a0[P0] * true)[rs1 ∪ rs0, f, g], ∀ r. r ∈ rs2 → r ∈ rs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
rs2 ∩ rs = ∅, rs1 ∩ rs0 = ∅, rs2 ∪ rs = rs1 ∪ rs0, a0[P0][rs2, f, g], R0[rs, f, g], a[P][rs1, f, g], R[rs0, f, g], r ∈ rs2 ⊦ # rs2 = 0, a0 = a, rs2 = ∅, (a[P] * a0[P0] * true)[rs1 ∪ rs0, f, g], r ∈ rs0

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ rs ≠ ∅ → # rs ≠ 0; (forward) from specification set-basic[refset]%ne-01: ⊦ r ∈ rs → rs ≠ ∅; (forward) from specification set-basic[refset]