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Proof step 21 from proof mod-other-both (previous step)

rs1 ∩ rs0 = ∅, P(mk(rs1, f)), R[rs0, f, g], r ∈ rs1, ∀ r. r ∈ rs1 → g(r) = a ⊦ g(r) = a, P(mk(rs1, f(r; o))), (a[P] * true)[rs1 ∪ rs0, f(r; o), g(r; a0)]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
rs1 ∩ rs0 = ∅, P(mk(rs1, f)), R[rs0, f, g], r ∈ rs1, ∀ r. r ∈ rs1 → g(r) = a ⊦ # rs1 = 0, g(r) = a, rs1 = ∅, P(mk(rs1, f(r; o))), (a[P] * true)[rs1 ∪ rs0, f(r; o), g(r; a0)]

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]