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Proof step 2 from proof at-unil (previous step)

rs0 ∩ rs1 = ∅, r ∈ rs0 ⊦ (mk(rs0, f0) ∪ mk(rs1, f1))[r] = f0(r)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
rs0 ∩ rs1 = ∅, r ∈ rs0 ⊦ # rs0 = 0, (mk(rs0, f0) ∪ mk(rs1, f1))[r] = f0(r), rs0 = ∅

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]