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Proof step 31 from proof rely-owned-unchgd (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
rs2 ∩ rs1 = ∅, a[P](mk(rs2, f, g)), ∀ r. (g(r) = a ∧ r ∈ rs2 ∪ rs1 ↔ g0(r) = a ∧ r ∈ rs0) ∧ (g(r) = a ∧ r ∈ rs2 ∪ rs1 → f(r) = f0(r)) ⊦ P(mk(rs2, f0)) ∧ (r ∈ rs2 → g0(r) = a)

Proof step 31 from proof rely-owned-unchgd (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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