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Proof step 15 from proof nodes-write-same-flushed (previous step)

gstore[m] = groupblock(gndx, lax, n0), gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][m1] = groupblock(gndx0, lax0, m4), m ∈ gstore, valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ (¬ m1 ∈ ginval → (m1 ∈ gstore ∧ @(m2, m3) ∈ lax0 ↔ @(m1, m2, m3) ∈ gstore ↓)) ∧ ( m1 ∈ gstore ∧ @(m2, m3) ∈ lax0 ∧ ¬ 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 16:
⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist
Proof step 17:
gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][m1] = groupblock(gndx0, lax0, m4), gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, valid-group-nodes(gndx) ≤ n0, n0 ≤ m0, valid-group-nodes(gndx) ≤ m0 ⊦ ( ¬ m1 ∈ ginval → ( m1 ∈ gstore ∧ @(m2, m3) ∈ lax0 ↔ @(m1, m2, m3).lnum ∈ gstore ↓ ∧ @(@(m1, m2, m3).pos, @(m1, m2, m3).size) ∈ gstore ↓[@(m1, m2, m3).lnum].ladrlist)) ∧ ( m1 ∈ gstore ∧ @(m2, m3) ∈ lax0 ∧ ¬ 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 ↓, @(m1, m2, m3)] flags: <all paths>

Additional information

Used terms: gstore ↓, @(m1, m2, m3)