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Proof step 5 from proof nodes-write-same-flushed (previous step)

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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, valid-group-nodes(gndx) ≤ n0, n0 ≤ m0, valid-group-nodes(gndx) ≤ m0 ⊦ ( ¬ adr.lnum ∈ ginval → (adr ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)] ↔ adr ∈ gstore ↓)) ∧ ( adr ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)] ∧ ¬ adr.lnum ∈ 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

Additional information

Used simplifier rules: nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);