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Proof step 37 from proof sep (previous step)

rs0 ∩ rs1 = ∅, P0(mk(rs0, f0)), P1(mk(rs1, f1)), r ∈ rs1, ∀ r0. (r0 ∈ rs ↔ r0 ∈ rs0 ∨ r0 ∈ rs1) ∧ (r0 ∈ rs → f(r0) = (mk(rs0, f0) ∪ mk(rs1, f1))[r0]) ⊦ # rs1 = 0, f(r) = f1(r), rs1 = ∅, P1(mk(rs1, f))

User applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: r abort: F discard: F computed: T

Additional information

Used simplifier rules: at-unir: ⊦ rs0 ∩ rs1 = ∅ ∧ r ∈ rs1 → (mk(rs0, f0) ∪ mk(rs1, f1))[r] = f1(r);%int-a: ⊦ (rs ∩ rs0) ∩ rs1 = rs ∩ rs0 ∩ rs1; from specification set-union[refset]%int-c: ⊦ rs ∩ rs0 = rs0 ∩ rs; from specification set-union[refset]% ⊦ rs ∩ rs0 = ∅ ∧ r ∈ rs → (r ∈ rs0 ↔ false); (as) Used terms: r