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Proof step 14 from proof gstore-dom-eq-hole (previous step)

gstore0 \ (∅ ++ n) = gstore1 \ (∅ ++ n), n ∈ gstore0, n0 ∈ gstore1, n0 ∈ gstore0 ⊦ gstore1[n0] = gstore0[n, gstore1[n]][n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ gstore = gstore0 ↔ (∀ n. (n ∈ gstore ↔ n ∈ gstore0) ∧ gstore[n] = gstore0[n])
Proof step 16:
n0 ∈ gstore0, n0 ∈ gstore1, n ∈ gstore0, ∀ n0. (n0 ∈ gstore0 \ (∅ ++ n) ↔ n0 ∈ gstore1 \ (∅ ++ n)) ∧ (gstore0 \ (∅ ++ n))[n0] = (gstore1 \ (∅ ++ n))[n0] ⊦ gstore1[n0] = gstore0[n, gstore1[n]][n0]

Rule argument

spec: store, inst: group-store-ablock-store-nat-store name: Extension seq: ⊦ gstore = gstore0 ↔ (∀ n. (n ∈ gstore ↔ n ∈ gstore0) ∧ gstore[n] = gstore0[n]) subst: [gstore0, gstore] → [gstore1 \ (∅ ++ n), gstore0 \ (∅ ++ n)] flags: <all paths>

Additional information

Used terms: gstore1 \ (∅ ++ n), gstore0 \ (∅ ++ n)