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Proof step 28 from proof nodes-no-change-eq (previous step)

gstore0[@(m, m0, m1)] = mkgnode(nd, m4, boolvar, boolvar0), gstore0[m] = groupblock(gndx0, lax0, m3), gstore1[m] = groupblock(gndx0, lax0, m2), gstore1[@(m, m0, m1)] = mkgnode(nd0, m5, boolvar1, boolvar2), @(m, m0, m1) ∈ gstore1, m ∈ gstore0, m ∈ gstore1, @(m0, m1) ∈ lax0, @(m, m0, m1) ∈ gstore0 ⊦ nd = nd0, m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ adr ∈ gstore → gstore[adr] = gstore[adr.lnum].gndlist[pos(@(adr.pos, adr.size), gstore[adr.lnum].ladrlist)]
Proof step 30:
gstore1[@(m, m0, m1).lnum].gndlist[pos(@(@(m, m0, m1).pos, @(m, m0, m1).size), gstore1[@(m, m0, m1).lnum].ladrlist)] = mkgnode(nd0, m5, boolvar1, boolvar2), gstore1[m] = groupblock(gndx0, lax0, m2), gstore0[m] = groupblock(gndx0, lax0, m3), gstore0[@(m, m0, m1)] = mkgnode(nd, m4, boolvar, boolvar0), @(m, m0, m1) ∈ gstore0, @(m0, m1) ∈ lax0, m ∈ gstore1, m ∈ gstore0, @(m, m0, m1) ∈ gstore1 ⊦ nd = nd0, m ∈ 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] → [@(m, m0, m1), gstore1] flags: <all paths>

Additional information

Used terms: @(m, m0, m1), gstore1