[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 39 from proof NEWPARTS-example (previous step)

P1 = pe(0, 2, 1) ' + pe(3, 5, 2) ', length_of_P = 2, F1 = (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1], Pdone = [], Pnew = [], p = P1.head, P = P1.tail, Pdone0 = Pdone + pe(p.first, p.first + (p.count - 1), 0) ' ∧ Pnew0 = Pnew + pe(p.first + p.count, p.last, 0) ' ∧ F = F1[p.first + p.count, p.last, length_of_P + # Pnew] ⊦ ⟨while P ≠ [] do let p = P.head in {P := P.tail; if p.count ≠ 0 ∧ p.first + p.count ≤ p.last then Pdone0 := Pdone0 + pe(p.first, p.first + (p.count - 1), 0) ', Pnew0 := Pnew0 + pe(p.first + p.count, p.last, 0) ', F := F[p.first + p.count, p.last, length_of_P + # Pnew0] else Pdone0 := Pdone0 + p '}⟩ ⟨P := Pdone0 + Pnew0⟩ ( P = pe(0, 0, 0) ' + pe(3, 4, 0) ' + pe(1, 2, 0) ' + pe(5, 5, 0) ' ∧ F = (∅)[0, 0][1, 2][2, 2][3, 1][4, 1][5, 3])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
length_of_P = 2, P = pe(3, 5, 2) ', Pdone0 = pe(0, 0, 0) ', Pnew0 = pe(1, 2, 0) ', F = (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1][1, 2, 2] ⊦ ⟨while P ≠ [] do let p = P.head in {P := P.tail; if p.count ≠ 0 ∧ p.first + p.count ≤ p.last then Pdone0 := Pdone0 + pe(p.first, p.first + (p.count - 1), 0) ', Pnew0 := Pnew0 + pe(p.first + p.count, p.last, 0) ', F := F[p.first + p.count, p.last, length_of_P + # Pnew0] else Pdone0 := Pdone0 + p '}⟩ ⟨P := Pdone0 + Pnew0⟩ ( P = pe(0, 0, 0) ' + pe(3, 4, 0) ' + pe(1, 2, 0) ' + pe(5, 5, 0) ' ∧ F = (∅)[0, 0][1, 2][2, 2][3, 1][4, 1][5, 3])

Rule argument

Additional information

[Concretesimprules((Csimpnamedseq(list-data,partition,size-01, ⊦ # [] = 0) Csimpnamedseq(partelem,,sel-04, ⊦ pe(m, m0, m1).last = m0) Csimpnamedseq(list,partition,Nil, ⊦ [] + P = P) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m) Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(partelem,,sel-05, ⊦ pe(m, m0, m1).count = m1) Csimpnamedseq(partelem,,sel-03, ⊦ pe(m, m0, m1).first = m) Csimpnamedseq(list,partition,c-08, ⊦ (p ' + P).head = p) Csimpnamedseq(list,partition,a, ⊦ (P + P0) + P1 = P + P0 + P1) Csimpnamedseq(list,partition,c-07, ⊦ (p ' + P).tail = P)))]