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Proof step 21 from proof rely-owned-unchgd (previous step)

rs2 ∩ rs1 = ∅, P(mk(rs2, f)), ∀ r. (g(r) = a ∧ r ∈ rs2 ∪ rs1 ↔ g0(r) = a ∧ r ∈ rs0) ∧ (g(r) = a ∧ r ∈ rs2 ∪ rs1 → f(r) = f0(r)), ∀ r. r ∈ rs2 → g(r) = a ⊦ rs2 ∪ (rs0 \ rs2) = rs0, ∀ r. r ∈ rs2 → r ∈ rs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
rs2 ∩ rs1 = ∅, P(mk(rs2, f)), r ∈ rs2, ∀ r. (g(r) = a ∧ r ∈ rs2 ∪ rs1 ↔ g0(r) = a ∧ r ∈ rs0) ∧ (g(r) = a ∧ r ∈ rs2 ∪ rs1 → f(r) = f0(r)), ∀ r. r ∈ rs2 → g(r) = a ⊦ # rs2 = 0, rs2 = ∅, rs2 ∪ (rs0 \ rs2) = rs0, 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]