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Proof step 8 from proof aux-known (previous step)

rs1 ∩ rs0 = ∅, a0[r => o][rs1, f, g], R[rs0, f, g] ⊦ (a1[r => o] * R)[rs1 ∪ rs0, f, g(r; a1)] ∧ g(r) = a0, a1[r => o][rs1, f, g(r; a1)] ∧ R[rs0, f, g(r; a1)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ R[rs, f, g] ↔ R(mk(rs, f, g))
Proof step 10:
rs1 ∩ rs0 = ∅, R[rs0, f, g], a0[r => o](mk(rs1, f, g)) ⊦ a1[r => o][rs1, f, g(r; a1)] ∧ R[rs0, f, g(r; a1)], (a1[r => o] * R)[rs1 ∪ rs0, f, g(r; a1)] ∧ g(r) = a0

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, a0[r => o]] flags: <all paths>

Additional information

Used terms: g, f, rs1, a0[r => o]