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Proof step 1 from proof down-store-write (conclusion)

⊦ gstore[m, gblock] ↓ = gstore ↓[m, gblock ↓]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ gstore = gstore0 ↔ (∀ n. (n ∈ gstore ↔ n ∈ gstore0) ∧ (n ∈ gstore → gstore[n] = gstore0[n]))
Proof step 3:
⊦ ∀ n. (n ∈ gstore[m, gblock] ↓ ↔ n ∈ gstore ↓[m, gblock ↓]) ∧ (n ∈ gstore[m, gblock] ↓ → gstore[m, gblock] ↓[n] = gstore ↓[m, gblock ↓][n])

Rule argument

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

Additional information

Used terms: gstore ↓[m, gblock ↓], gstore[m, gblock] ↓