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Proof step 19 from proof merge-owned (previous step)

rs1 ∩ rs0 = ∅, rs2 ∩ rs = ∅, rs2 ∪ rs = rs1 ∪ rs0, R[rs0, f, g], a[P][rs1, f, g], R0[rs, f, g], a0[P0][rs2, f, g] ⊦ a0 = a, (a[P] * a0[P0] * true)[rs1 ∪ rs0, f, g], rs2 ⊆ rs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ rs ⊆ rs0 ↔ (∀ r. r ∈ rs → r ∈ rs0)
Proof step 21:
rs2 ∩ rs = ∅, rs1 ∩ rs0 = ∅, rs2 ∪ rs = rs1 ∪ rs0, a0[P0][rs2, f, g], R0[rs, f, g], a[P][rs1, f, g], R[rs0, f, g] ⊦ a0 = a, (a[P] * a0[P0] * true)[rs1 ∪ rs0, f, g], ∀ r. r ∈ rs2 → r ∈ rs0

Rule argument

spec: set-basic, inst: refset name: Subset seq: ⊦ rs ⊆ rs0 ↔ (∀ r. r ∈ rs → r ∈ rs0) subst: [rs0, rs] → [rs0, rs2] flags: <all paths>

Additional information

Used terms: rs0, rs2