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Proof step 6 from proof down-store-at-diff (previous step)

⊦ (gstore \ ginval)↓[n] = gstore ↓[n], n ∈ ginval, n ∈ gstore

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n]
Proof step 8:
⊦ (∅)[n] = gstore ↓[n], n ∈ gstore, n ∈ ginval, n ∈ (gstore \ ginval)↓

Rule argument

spec: store, inst: group-store-ablock-store-nat-store name: notmemlookup seq: ⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n] subst: [n, gstore] → [n, (gstore \ ginval)↓] flags: <all paths>

Additional information

Used simplifier rules: down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;% ⊦ n ∈ gstore \ ns ↔ n ∈ gstore ∧ ¬ n ∈ ns; (ws) Used terms: n, (gstore \ ginval)↓