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Proof step 27 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)] = mkgnode(nd, m4, boolvar, boolvar0), transaction(ndx, gndx1), n ∈ gstore ⊦ nd = ndx[pos(@(n, m2, m3), @(n, m2, m3) ' + lax0.to-adr(n)) + # lax2.to-adr(n)], 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, @(n, m2, m3) ∈ lax2.to-adr(n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# 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[# lax2], 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: ⊦ @(n0, n1, n2) ∈ lax.to-adr(n) ↔ n0 = n ∧ @(n1, n2) ∈ lax; (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)% ⊦ # lax.to-adr(n) = # lax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ pos(adr, adr ' + ax) = 0; (s)