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Proof step 22 from proof lift-unknown (previous step)

rs1 ∩ rs0 = ∅, r ==>(o, a)(mk(rs1, f, g)), R[rs0, f, g] ⊦ ∃ o. (a[r => o] * R)[rs1 ∪ rs0, f, g], (∃ o. ((r => o))(mk(rs1, f))) ∧ (r0 ∈ rs1 → g(r0) = a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ r ==>(o, a)(Ha) ↔ Ha = (∅ ++ r)[r, o, a] ∧ r ≠ null
Proof step 24:
mk(rs1, f, g) = (∅ ++ r)[r, o, a], rs1 ∩ rs0 = ∅, R[rs0, f, g] ⊦ r = null, ∃ o. (a[r => o] * R)[rs1 ∪ rs0, f, g], (∃ o. ((r => o))(mk(rs1, f))) ∧ (r0 ∈ rs1 → g(r0) = a)

Rule argument

spec: maplet, inst: heap-aux name: maplet seq: ⊦ r ==>(o, a)(Ha) ↔ Ha = (∅ ++ r)[r, o, a] ∧ r ≠ null subst: [Ha, a, o, r] → [mk(rs1, f, g), a, o, r] flags: <all paths>

Additional information

Used terms: mk(rs1, f, g), a, o, r