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Proof step 82 from proof embed-split (previous step)

mk(rs, f, g) = mk(rs0, f0, g0) ∪ mk(rs1, f1, g1), rs0 ∩ rs1 = ∅, P0(mk(rs0, f0)), P1(mk(rs1, f1)), r ∈ rs, r ∈ rs1 → g1(r) = a, ∀ r. r ∈ rs1 → g1(r) = a, ∀ r. r ∈ rs0 → g0(r) = a ⊦ # rs = 0, g(r) = a, rs = ∅

User applied rule all left

And obtained the following new goals

Proof step 83:
mk(rs, f, g) = mk(rs0, f0, g0) ∪ mk(rs1, f1, g1), rs0 ∩ rs1 = ∅, P0(mk(rs0, f0)), P1(mk(rs1, f1)), r ∈ rs, r ∈ rs1 → g1(r) = a, r ∈ rs0 → g0(r) = a, ∀ r. r ∈ rs0 → g0(r) = a, ∀ r. r ∈ rs1 → g1(r) = a ⊦ # rs = 0, g(r) = a, rs = ∅

Rule argument

pos: left 8 terms: r abort: F discard: F computed: T

Additional information

Used terms: r