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Proof step 9 from proof nodes-append-subseteq-nodown (previous step)

# gndx1 = # lax1, # gndx = # lax, gstore[n] = groupblock(gndx, lax, m0), gstore[m] ↓ = groupblock(gndx0, lax0, m3), @(m1, m2) ∈ lax0, m ∈ gstore, n ∈ gstore ⊦ m ∈ ginval, @(m, m1, m2) ∈ gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)] ∧ nodes(gstore ↓, ginval)[@(m, m1, m2)] = nodes(gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)], ginval)[@(m, m1, m2)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist
Proof step 11:
# gndx = # lax, # gndx1 = # lax1, gstore[n] = groupblock(gndx, lax, m0), gstore[m] ↓ = groupblock(gndx0, lax0, m3), n ∈ gstore, m ∈ gstore, @(m1, m2) ∈ lax0 ⊦ m ∈ ginval, ( @(m, m1, m2).lnum ∈ gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)] ∧ @(@(m, m1, m2).pos, @(m, m1, m2).size) ∈ gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)][@(m, m1, m2).lnum].ladrlist) ∧ nodes(gstore ↓, ginval)[@(m, m1, m2)] = nodes(gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)], ginval)[@(m, m1, m2)]

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 ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)], @(m, m1, m2)] flags: <all paths>

Additional information

Used terms: gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)], @(m, m1, m2)