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Proof step 20 from proof nodes-cons-write-other (previous step)

# ax = # ndx, gstore[n] = groupblock(gndx, lax0, m3), ax[n0] = @(n, m1, m2), gstore[n, groupblock(gndx, lax0, m)][@(n, m1, m2)] = mkgnode(nd, m4, boolvar, boolvar0), gstore[@(n, m1, m2)] = mkgnode(ndx[n0], m5, boolvar1, boolvar2), n0 < # ndx, @(n, m1, m2) ∈ gstore ⊦ nd = ndx[n0], ndx = [], n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ adr ∈ gstore → gstore[adr] = gstore[adr.lnum].gndlist[pos(@(adr.pos, adr.size), gstore[adr.lnum].ladrlist)]
Proof step 22:
# ax = # ndx, gstore[@(n, m1, m2)] = mkgnode(ndx[n0], m5, boolvar1, boolvar2), gstore[n, groupblock(gndx, lax0, m)][@(n, m1, m2).lnum].gndlist [pos(@(@(n, m1, m2).pos, @(n, m1, m2).size), gstore[n, groupblock(gndx, lax0, m)][@(n, m1, m2).lnum].ladrlist) ] = mkgnode(nd, m4, boolvar, boolvar0), ax[n0] = @(n, m1, m2), gstore[n] = groupblock(gndx, lax0, m3), n0 < # ndx, @(n, m1, m2) ∈ gstore, @(n, m1, m2) ∈ gstore[n, groupblock(gndx, lax0, m)] ⊦ nd = ndx[n0], ndx = [], 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, lax0, m)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ @(n, n0, n1) ∈ gstore[n, gblock] ↔ @(n0, n1) ∈ gblock.ladrlist; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)%⊦ gstore[n] = groupblock(gndx, lax, m0) ∧ @(n, n0, n1) ∈ gstore → @(n0, n1) ∈ lax; (ss) Used terms: @(n, m1, m2), gstore[n, groupblock(gndx, lax0, m)]