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Proof step 21 from proof gstore-dom-eq-hole (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: group-store-ablock-store-nat-store name: Diff-get seq: ⊦ ¬ n ∈ ns → (gstore \ ns)[n] = gstore[n] subst: [n, ns, gstore] → [n0, ∅ ++ n, gstore1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ n ∈ ns → (gstore \ ns)[n] = gstore[n]; (s)% ⊦ n ∈ ns → (gstore \ ns)[n] = (∅)[n]; (s)% ⊦ n ∈ ∅ ++ n0 ↔ n = n0; (s) Used terms: n0, ∅ ++ n, gstore1