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Proof step 9 from proof lift-unknown (previous step)

rs1 ∩ rs0 = ∅, r ==>(o, a)[rs1, f, g], R[rs0, f, g] ⊦ (a[r =>_] * R)[rs1 ∪ rs0, f, g]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ R0[rs0, f, g] ∧ R1[rs1, f, g] ∧ rs0 ∩ rs1 = ∅ → (R0 * R1)[rs0 ∪ rs1, f, g]
Proof step 11:
rs1 ∩ rs0 = ∅, R[rs0, f, g], r ==>(o, a)[rs1, f, g] ⊦ (a[r =>_] * R)[rs1 ∪ rs0, f, g], a[r =>_][rs1, f, g] ∧ R[rs0, f, g] ∧ rs1 ∩ rs0 = ∅

Rule argument

spec: heap-fun, inst: heap-aux name: split-uni seq: ⊦ R0[rs0, f, g] ∧ R1[rs1, f, g] ∧ rs0 ∩ rs1 = ∅ → (R0 * R1)[rs0 ∪ rs1, f, g] subst: [g, f, rs1, rs0, R1, R0] → [g, f, rs0, rs1, R, a[r =>_]] flags: <all paths>

Additional information

Used terms: g, f, rs0, rs1, R, a[r =>_]