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Proof step 113 from proof write-known (previous step)

mk(rs1, f(r; o1)) = (∅ ++ r)[r, o1], rs1 ∩ rs0 = ∅, R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ mk(rs1, f) = (∅ ++ r)[r, f(r)], r = null, (a[r => f(r)] * R)[rs1 ∪ rs0, f, g], r ∈ rs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 114:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 115:
rs1 ∩ rs0 = ∅, R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a, ∀ r0. (r0 ∈ mk(rs1, f(r; o1)) ↔ r0 ∈ (∅ ++ r)[r, o1]) ∧ (r0 ∈ mk(rs1, f(r; o1)) → mk(rs1, f(r; o1))[r0] = (∅ ++ r)[r, o1][r0]) ⊦ mk(rs1, f) = (∅ ++ r)[r, f(r)], r = null, (a[r => f(r)] * R)[rs1 ∪ rs0, f, g], r ∈ rs0

Rule argument

spec: heap name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [(∅ ++ r)[r, o1], mk(rs1, f(r; o1))] flags: <all paths>

Additional information

Used terms: (∅ ++ r)[r, o1], mk(rs1, f(r; o1))