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Proof step 36 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 ⊦ P(mk(rs2, f0))

User applied rule cut formula

And obtained the following new goals

Proof step 37:
rs2 ∩ rs1 = ∅, P(mk(rs2, f)), ∀ r. r ∈ rs2 → g(r) = a, ∀ r. (g(r) = a ∧ r ∈ rs2 ∪ rs1 ↔ g0(r) = a ∧ r ∈ rs0) ∧ (g(r) = a ∧ r ∈ rs2 ∪ rs1 → f(r) = f0(r)) ⊦ mk(rs2, f0) = mk(rs2, f), P(mk(rs2, f0))

Rule argument

fma: mk(rs2, f0) = mk(rs2, f)

Additional information

Used formulas: mk(rs2, f0) = mk(rs2, f)