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Proof step 14 from proof rely-owned-unchgd (previous step)

rs2 ∩ rs1 = ∅, a[P][rs2, f, g], ∀ r. (g(r) = a ∧ r ∈ rs2 ∪ rs1 ↔ g0(r) = a ∧ r ∈ rs0) ∧ (g(r) = a ∧ r ∈ rs2 ∪ rs1 → f(r) = f0(r)) ⊦ rs2 ∪ (rs0 \ rs2) = rs0, rs2 ⊆ rs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ R[rs, f, g] ↔ R(mk(rs, f, g))
Proof step 16:
rs2 ∩ rs1 = ∅, a[P](mk(rs2, f, g)), ∀ r. (g(r) = a ∧ r ∈ rs2 ∪ rs1 ↔ g0(r) = a ∧ r ∈ rs0) ∧ (g(r) = a ∧ r ∈ rs2 ∪ rs1 → f(r) = f0(r)) ⊦ rs2 ∪ (rs0 \ rs2) = rs0, rs2 ⊆ rs0

Rule argument

spec: heap-fun, inst: heap-aux name: apply seq: ⊦ R[rs, f, g] ↔ R(mk(rs, f, g)) subst: [g, f, rs, R] → [g, f, rs2, a[P]] flags: <all paths>

Additional information

Used terms: g, f, rs2, a[P]