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Proof step 33 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)][@(m, m2, m3)] = mkgnode(nd, m1, boolvar, boolvar0), gstore ↓[@(m, m2, m3)] = mkgnode(nd0, m4, boolvar1, boolvar2), @(m2, m3) ∈ prefixn(valid-group-nodes(gndx), lax), m ∈ gstore, valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ nd = nd0, m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ adr ∈ gstore → gstore[adr] = gstore[adr.lnum].gndlist[pos(@(adr.pos, adr.size), gstore[adr.lnum].ladrlist)]
Proof step 35:
gstore ↓[@(m, m2, m3)] = mkgnode(nd0, m4, boolvar1, boolvar2), gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][@(m, m2, m3).lnum].gndlist [pos (@(@(m, m2, m3).pos, @(m, m2, m3).size), gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][@(m, m2, m3).lnum].ladrlist) ] = mkgnode(nd, m1, boolvar, boolvar0), gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, @(m2, m3) ∈ prefixn(valid-group-nodes(gndx), lax), @(m, m2, m3) ∈ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], valid-group-nodes(gndx) ≤ n0, n0 ≤ m0, valid-group-nodes(gndx) ≤ m0 ⊦ 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, m2, m3), gstore ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), 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) Used terms: @(m, m2, m3), gstore ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0) ]