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Proof step 25 from proof embed-split (previous step)

rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0(mk(rs1, f)), P1[rs0, f], ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g)), a[P0](mk(rs1, f, g)) ∧ a[P1](mk(rs0, f, g))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ P[rs, f] ↔ P(mk(rs, f))
Proof step 27:
rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0(mk(rs1, f)), P1(mk(rs0, f)), ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g)), a[P0](mk(rs1, f, g)) ∧ a[P1](mk(rs0, f, g))

Rule argument

spec: heap-fun name: apply seq: ⊦ P[rs, f] ↔ P(mk(rs, f)) subst: [f, rs, P] → [f, rs0, P1] flags: <all paths>

Additional information

Used terms: f, rs0, P1