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Proof step 3 from proof nodes-write-same-flushed (previous step)

gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, valid-group-nodes(gndx) ≤ n0, n0 ≤ m0, valid-group-nodes(gndx) ≤ m0 ⊦ nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval) = nodes(gstore ↓, ginval)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ fs = fs0 ↔ (∀ adr. (adr ∈ fs ↔ adr ∈ fs0) ∧ (adr ∈ fs → fs[adr] = fs0[adr]))
Proof step 5:
gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ ∀ adr. ( adr ∈ nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval) ↔ adr ∈ nodes(gstore ↓, ginval)) ∧ ( adr ∈ nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval) → nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval)[adr] = nodes(gstore ↓, ginval)[adr])

Rule argument

spec: store, inst: node-store name: k-Extension seq: ⊦ fs = fs0 ↔ (∀ adr. (adr ∈ fs ↔ adr ∈ fs0) ∧ (adr ∈ fs → fs[adr] = fs0[adr])) subst: [fs0, fs] → [nodes(gstore ↓, ginval), nodes (gstore ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0) ], ginval)] flags: <all paths>

Additional information

Used terms: nodes(gstore ↓, ginval), nodes (gstore ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0) ], ginval)