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Proof step 52 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, a[r => o0][rs1, f, g], R[rs0, f, g], r ∈ rs0 ⊦ # rs0 = 0, rs0 = ∅, R[rs0, f(r; o1), g], (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g] ∧ f(r) = o0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ R[rs, f, g] ↔ R(mk(rs, f, g))
Proof step 54:
rs1 ∩ rs0 = ∅, R[rs0, f, g], a[r => o0](mk(rs1, f, g)), r ∈ rs0 ⊦ # rs0 = 0, rs0 = ∅, R[rs0, f(r; o1), g], (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g] ∧ f(r) = o0

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, rs1, a[r => o0]] flags: <all paths>

Additional information

Used terms: g, f, rs1, a[r => o0]