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Proof step 51 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, a[r => o0][rs1, f, g], R[rs0, f, g], r ∈ rs0 ⊦ R[rs0, f(r; o1), g], (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g] ∧ f(r) = o0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
rs1 ∩ rs0 = ∅, a[r => o0][rs1, f, g], R[rs0, f, g], r ∈ rs0 ⊦ # rs0 = 0, rs0 = ∅, R[rs0, f(r; o1), g], (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g] ∧ f(r) = o0

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]