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Proof step 56 from proof aux-known (previous step)

rs1 ∩ rs0 = ∅, R[rs0, f, g(r; a1)], a1[r => o][rs1, f, g(r; a1)], r ∈ rs0 ⊦ # rs0 = 0, rs0 = ∅, (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o][rs1, f, g] ∧ R[rs0, f, g]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ R[rs, f, g] ↔ R(mk(rs, f, g))
Proof step 58:
rs1 ∩ rs0 = ∅, a1[r => o](mk(rs1, f, g(r; a1))), R[rs0, f, g(r; a1)], r ∈ rs0 ⊦ # rs0 = 0, rs0 = ∅, (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o][rs1, f, g] ∧ R[rs0, f, g]

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(r; a1), f, rs1, a1[r => o]] flags: <all paths>

Additional information

Used terms: g(r; a1), f, rs1, a1[r => o]