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Proof step 26 from proof nodes-append-subseteq-nodown (previous step)

# gndx1 = # lax1, # gndx = # lax, gstore[n] = groupblock(gndx, lax, m0), prefixn(valid-group-nodes(gndx), gndx)[pos(@(m1, m2), lax)] = mkgnode(nd, m5, boolvar, boolvar0), gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)][@(n, m1, m2)] = mkgnode(nd0, m, boolvar1, boolvar2), @(m1, m2) ∈ lax, @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), n ∈ gstore ⊦ nd = nd0, n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ adr ∈ gstore → gstore[adr] = gstore[adr.lnum].gndlist[pos(@(adr.pos, adr.size), gstore[adr.lnum].ladrlist)]
Proof step 28:
# gndx = # lax, # gndx1 = # lax1, gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)][@(n, m1, m2).lnum].gndlist [pos(@(@(n, m1, m2).pos, @(n, m1, m2).size), gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)][@(n, m1, m2).lnum].ladrlist) ] = mkgnode(nd0, m, boolvar1, boolvar2), prefixn(valid-group-nodes(gndx), gndx)[pos(@(m1, m2), lax)] = mkgnode(nd, m5, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m0), n ∈ gstore, @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), @(m1, m2) ∈ lax, @(n, m1, m2) ∈ gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)] ⊦ nd = nd0, n ∈ ginval

Rule argument

spec: ablock-store-inv, inst: group-store name: at seq: ⊦ adr ∈ gstore → gstore[adr] = gstore[adr.lnum].gndlist [pos(@(adr.pos, adr.size), gstore[adr.lnum].ladrlist) ] subst: [adr, gstore] → [@(n, m1, m2), gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)]] flags: <all paths>

Additional information

Used simplifier rules: down-store-write-same: ⊦ @(n, n0, n1) ∈ gstore ↓[n, gblock] ↔ @(n0, n1) ∈ gblock.ladrlist;% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ ladr ∈ lax → ladr ∈ lax + lax0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list] Used terms: @(n, m1, m2), gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)]