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Proof step 50 from proof embed-split (previous step)

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)) ⊦ ((P0 * P1))(mk(rs, f)) ∧ (r ∈ rs → g(r) = a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1))
Proof step 52:
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)

Rule argument

spec: heap-sep name: sep seq: ⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1)) subst: [H, P1, P0] → [mk(rs, f), P1, P0] flags: <all paths>

Additional information

Used terms: mk(rs, f), P1, P0