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Proof step 77 from proof aux-known (previous step)

mk(rs1, f) = (∅ ++ r)[r, o], rs1 ∩ rs0 = ∅, R[rs0, f, g], ∀ r0. r0 ∈ rs1 → (r = r0 ⊃ a1;g(r0)) = a1 ⊦ r = null, g(r)[r => o][rs1, f, g], (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], r ∈ rs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
⊦ R[rs, f, g] ↔ R(mk(rs, f, g))
Proof step 79:
mk(rs1, f) = (∅ ++ r)[r, o], rs1 ∩ rs0 = ∅, R[rs0, f, g], ∀ r0. r0 ∈ rs1 → (r = r0 ⊃ a1;g(r0)) = a1 ⊦ r = null, (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o](mk(rs1, 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, g(r)[r => o]] flags: <all paths>

Additional information

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