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Proof step 55 from proof aux-known (previous step)

rs1 ∩ rs0 = ∅, R[rs0, f, g(r; a1)], a1[r => o][rs1, f, g(r; a1)], r ∈ rs0 ⊦ (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o][rs1, f, g] ∧ R[rs0, f, g]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
rs1 ∩ rs0 = ∅, R[rs0, f, g(r; a1)], a1[r => o][rs1, f, g(r; a1)], r ∈ rs0 ⊦ # rs0 = 0, rs0 = ∅, (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o][rs1, f, g] ∧ R[rs0, f, g]

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]