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Proof step 100 from proof write-known (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 101:
⊦ R[rs, f, g] ↔ R(mk(rs, f, g))
Proof step 102:
rs1 ∩ rs0 = ∅, R[rs0, f, g], a[r => o1][rs1, f(r; o1), g] ⊦ a[r => f(r)](mk(rs1, f, g)), (a[r => f(r)] * R)[rs1 ∪ rs0, f, g], r ∈ 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, rs1, a[r => f(r)]] flags: <all paths>

Additional information

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