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Proof step 52 from proof embed-split (previous step)

mk(rs, f, g) = mk(rs0, f0, g0) ∪ mk(rs1, f1, g1), rs0 ∩ rs1 = ∅, a[P1](mk(rs1, f1, g1)), a[P0](mk(rs0, f0, g0)) ⊦ (∃ H0, H1. H0 ⊥ H1 ∧ mk(rs, f) = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1)) ∧ (r ∈ rs → g(r) = a)

User applied rule case distinction

And obtained the following new goals

Proof step 53:
mk(rs, f, g) = mk(rs0, f0, g0) ∪ mk(rs1, f1, g1), rs0 ∩ rs1 = ∅, a[P0](mk(rs0, f0, g0)), a[P1](mk(rs1, f1, g1)) ⊦ ∃ H0, H1. H0 ⊥ H1 ∧ mk(rs, f) = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1)
Proof step 74:
mk(rs, f, g) = mk(rs0, f0, g0) ∪ mk(rs1, f1, g1), rs0 ∩ rs1 = ∅, a[P0](mk(rs0, f0, g0)), a[P1](mk(rs1, f1, g1)), r ∈ rs ⊦ g(r) = a

Rule argument

pos: right 1

Proof step 52 from proof embed-split (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information