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Proof step 50 from proof rely-owned-unchgd (previous step)

rs2 ∩ rs1 = ∅, a[P][rs2, f0, g0], ∀ r. (g(r) = a ∧ r ∈ rs ↔ g0(r) = a ∧ r ∈ rs2 ∪ rs1) ∧ (g(r) = a ∧ r ∈ rs → f(r) = f0(r)) ⊦ (a[P] * true)[rs, f, g]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ (R0 * R1)[rs, f, g] ↔ (∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ R0[rs0, f, g] ∧ R1[rs1, f, g])
Proof step 52:
rs2 ∩ rs1 = ∅, a[P][rs2, f0, g0], ∀ r. (g(r) = a ∧ r ∈ rs ↔ g0(r) = a ∧ r ∈ rs2 ∪ rs1) ∧ (g(r) = a ∧ r ∈ rs → f(r) = f0(r)) ⊦ ∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ a[P][rs0, f, g] ∧ (true)[rs1, f, g]

Rule argument

spec: heap-fun, inst: heap-aux name: sep seq: ⊦ (R0 * R1)[rs, f, g] ↔ (∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ R0[rs0, f, g] ∧ R1[rs1, f, g]) subst: [g, f, rs, R1, R0] → [g, f, rs, true, a[P]] flags: <all paths>

Additional information

Used terms: g, f, rs, true, a[P]