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Proof step 7 from proof gstore-dom-eq-hole (previous step)

gstore0 \ (∅ ++ n) = gstore1 \ (∅ ++ n), dom gstore0 = dom gstore1, n ∈ gstore0 ⊦ (n0 ∈ gstore1 ↔ n0 ∈ gstore0[n, gstore1[n]]) ∧ (n0 ∈ gstore1 → gstore1[n0] = gstore0[n, gstore1[n]][n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ∈ gstore[n0, gblock] ↔ n = n0 ∨ n ∈ gstore
Proof step 9:
gstore0 \ (∅ ++ n) = gstore1 \ (∅ ++ n), dom gstore0 = dom gstore1, n ∈ gstore0 ⊦ (n0 ∈ gstore1 ↔ n0 = n ∨ n0 ∈ gstore0) ∧ (n0 ∈ gstore1 → gstore1[n0] = gstore0[n, gstore1[n]][n0])

Rule argument

spec: store, inst: group-store-ablock-store-nat-store name: In-insert seq: ⊦ n ∈ gstore[n0, gblock] ↔ n = n0 ∨ n ∈ gstore subst: [gblock, n0, gstore, n] → [gstore1[n], n, gstore0, n0] flags: <all paths>

Additional information

Used terms: gstore1[n], n, gstore0, n0