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Proof step 21 from proof nodes-transaction (previous step)

# lax = # gndx, # lax1 = # gndx1, # lax1.to-adr(n) = # ndx, 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, @(m2, m3) ∈ lax1, @(n, m2, m3) ∈ lax1.to-adr(n) ⊦ nd = ndx[pos(@(n, m2, m3), lax1.to-adr(n))], dups(lax + lax1), dups(lax), dups(lax1), dups(lax1.to-adr(n)), n ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
# ndx = # gndx1, # lax = # gndx, # lax1 = # gndx1, gstore[n] = groupblock(gndx, lax, m), gstore[n, groupblock(gndx + gndx1, lax + lax1, m0)][@(n, m2, m3)] = mkgnode(nd, m4, boolvar, boolvar0), transaction(ndx, gndx1), @(m2, m3) ∈ lax1, n ∈ gstore ⊦ nd = ndx[pos(@(n, m2, m3), lax1.to-adr(n))], dups(lax), dups(lax + lax1), dups(lax1), n ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ dups(lax.to-adr(n)) ↔ dups(lax); (s)% ⊦ @(m, m0, m1) ∈ lax.to-adr(n) ↔ m = n ∧ @(m0, m1) ∈ lax; (ws)% ⊦ # lax.to-adr(n) = # lax; (s)