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Proof step 8 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 ⊦ ( ¬ m1 ∈ ginval → ( @(m1, m2, m3) ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)] ↔ @(m1, m2, m3) ∈ gstore ↓)) ∧ ( @(m1, m2, m3) ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)] ∧ ¬ m1 ∈ ginval → nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval)[@(m1, m2, m3)] = nodes(gstore ↓, ginval)[@(m1, m2, m3)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist
Proof step 10:
gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ ( ¬ m1 ∈ ginval → ( @(m1, m2, m3).lnum ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)] ∧ @(@(m1, m2, m3).pos, @(m1, m2, m3).size) ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][@(m1, m2, m3).lnum].ladrlist ↔ @(m1, m2, m3) ∈ gstore ↓)) ∧ ( ( @(m1, m2, m3).lnum ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)] ∧ @(@(m1, m2, m3).pos, @(m1, m2, m3).size) ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][@(m1, m2, m3).lnum].ladrlist) ∧ ¬ m1 ∈ ginval → nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval)[@(m1, m2, m3)] = nodes(gstore ↓, ginval)[@(m1, m2, m3)])

Rule argument

spec: ablock-store-inv, inst: group-store name: in seq: ⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist subst: [gstore, adr] → [gstore ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0) ], @(m1, m2, m3)] flags: <all paths>

Additional information

Used terms: gstore ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0) ], @(m1, m2, m3)