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Proof step 30 from proof nodes-transaction (previous step)

# ndx = # gndx1, # lax = # gndx, # lax2 + # lax0 + 1 = # gndx1, gstore[n] = groupblock(gndx, lax, m), gstore[n, groupblock(gndx + gndx1, lax + lax2 + @(m2, m3) ' + lax0, m0)][@(n, m2, m3).lnum].gndlist [pos(@(@(n, m2, m3).pos, @(n, m2, m3).size), gstore[n, groupblock(gndx + gndx1, lax + lax2 + @(m2, m3) ' + lax0, m0)][@(n, m2, m3).lnum].ladrlist) ] = mkgnode(nd, m4, boolvar, boolvar0), transaction(ndx, gndx1), n ∈ gstore, @(n, m2, m3) ∈ gstore[n, groupblock(gndx + gndx1, lax + lax2 + @(m2, m3) ' + lax0, m0)] ⊦ nd = ndx[# lax2], dups(lax2), dups(lax), dups((lax + lax2) + lax0), dups(lax2 + lax0), dups(lax0), dups(lax + lax2), n ∈ ginval, @(m2, m3) ∈ lax, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# ndx = # gndx1, # lax = # gndx, # lax2 + # lax0 + 1 = # gndx1, gstore[n] = groupblock(gndx, lax, m), gndx1[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), transaction(ndx, gndx1), n ∈ gstore ⊦ nd = ndx[# lax2], dups(lax2), dups(lax), dups((lax + lax2) + lax0), dups(lax2 + lax0), dups(lax0), dups(lax + lax2), n ∈ ginval, @(m2, m3) ∈ lax, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ (gndx + gndx0)[n + # gndx] = gndx0[n]; (s)% ⊦ ¬ ladr ∈ lax → (ladr ∈ ladr0 ' + lax ↔ ladr = ladr0); (s)% ⊦ ladr ∈ lax + lax0 ↔ ladr ∈ lax ∨ ladr ∈ lax0; (s)% ⊦ @(n, n0, n1) ∈ gstore[n, gblock] ↔ @(n0, n1) ∈ gblock.ladrlist; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ pos(ladr, ladr ' + lax) = 0; (s)% ⊦ ¬ ladr ∈ lax → pos(ladr, lax + lax0) = pos(ladr, lax0) + # lax; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ gstore[n, gblock][n] = gblock; (s)% ⊦ @(m, m0, m1).lnum = m; (s)