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Proof step 17 from proof lift-unknown (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ r =>_ = _∃(λ o. r => o)
Proof step 19:
rs1 ∩ rs0 = ∅, r ==>(o, a)[rs1, f, g], R[rs0, f, g] ⊦ (a[_∃(λ o. r => o)] * R)[rs1 ∪ rs0, f, g], (_∃(λ o. r => o))(mk(rs1, f)) ∧ (r0 ∈ rs1 → g(r0) = a)

Rule argument

spec: maplet name: mapex seq: ⊦ r =>_ = _∃(λ o. r => o) subst: [r] → [r] flags: <all paths>

Additional information

Used terms: r