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Proof step 24 from proof nodes-transaction (previous step)

# lax1 = # gndx1, # lax = # gndx, # ndx = # gndx1, gstore[n, groupblock(gndx + gndx1, lax + lax1, m0)][@(n, m2, m3)] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), transaction(ndx, gndx1), n ∈ gstore, ∃ lax0, lax2. lax1 = lax0 + (@(m2, m3) + lax2) ⊦ nd = ndx[pos(@(n, m2, m3), lax1.to-adr(n))], dups(lax1), dups(lax + lax1), dups(lax), n ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# lax = # gndx, # ndx = # gndx1, # lax2 + # lax0 + 1 = # gndx1, gstore[n, groupblock(gndx + gndx1, lax + lax2 + @(m2, m3) ' + lax0, m0)][@(n, m2, m3)] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), transaction(ndx, gndx1), n ∈ gstore ⊦ nd = ndx[pos(@(n, m2, m3), lax2.to-adr(n) + @(n, m2, m3) ' + lax0.to-adr(n))], dups(lax + lax2), dups(lax0), dups(lax2 + lax0), dups((lax + lax2) + lax0), dups(lax), dups(lax2), @(m2, m3) ∈ lax0, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax, n ∈ ginval

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]%⊦ ¬ ladr ∈ lax ∧ ¬ ladr ∈ lax0 → (dups(lax + ladr ' + lax0) ↔ dups(lax + lax0)); (s)% ⊦ ladr ∈ lax + lax0 ↔ ladr ∈ lax ∨ ladr ∈ lax0; (s)%⊦ dups(lax + ladr ' + lax0) ↔ ladr ∈ lax ∨ ladr ∈ lax0 ∨ dups(lax + lax0); (ws)% ⊦ adr + ax = adr ' + ax; (s)% ⊦ @(m, m0).size = m0; (s)% ⊦ @(m, m0).off = m; (s)%⊦ (ladr ' + lax).to-adr(n) = @(n, ladr.off, ladr.size) + lax.to-adr(n); (s)% ⊦ (lax0 + lax1).to-adr(n) = lax0.to-adr(n) + lax1.to-adr(n); (s)% ⊦ m +1 = m + 1; (s)% ⊦ #(ladr ' + lax) = (# lax)+1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ ladr + lax = ladr ' + lax; (s)