[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 47 from proof NEWPARTS-example (previous step)

P = pe(0, 2, 1) ' + pe(3, 5, 2) ', F = (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1] ⊦ ⟨let Pdone = [], Pnew = [], length_of_P = # P in {F0 := F, P0 := P; while P0 ≠ [] do let p = P0.head in {P0 := P0.tail; if p.count ≠ 0 ∧ p.first + p.count ≤ p.last then Pdone := Pdone + pe(p.first, p.first + p.count -1, 0), Pnew := Pnew + pe(p.first + p.count, p.last, 0), F0 := F0[p.first + p.count, p.last, length_of_P + # Pnew] else Pdone := Pdone + p}; P0 := Pdone + Pnew}⟩ ( P0 = pe(0, 0, 0) ' + pe(3, 4, 0) ' + pe(1, 2, 0) ' + pe(5, 5, 0) ' ∧ F0 = (∅)[0, 0][1, 2][2, 2][3, 1][4, 1][5, 3])

Heuristic symbolic execution applied rule vardecls right

And obtained the following new goals

Proof step 46:
P = pe(0, 2, 1) ' + pe(3, 5, 2) ', F = (∅)[0, 0][1, 0][2, 0][3, 1][4, 1][5, 1], length_of_P = # P, Pnew = [], Pdone = [] ⊦ ⟨F0 := F, P0 := P⟩ ⟨while P0 ≠ [] do let p = P0.head in {P0 := P0.tail; if p.count ≠ 0 ∧ p.first + p.count ≤ p.last then Pdone := Pdone + pe(p.first, p.first + p.count -1, 0), Pnew := Pnew + pe(p.first + p.count, p.last, 0), F0 := F0[p.first + p.count, p.last, length_of_P + # Pnew] else Pdone := Pdone + p}⟩ ⟨P0 := Pdone + Pnew⟩ ( P0 = pe(0, 0, 0) ' + pe(3, 4, 0) ' + pe(1, 2, 0) ' + pe(5, 5, 0) ' ∧ F0 = (∅)[0, 0][1, 2][2, 2][3, 1][4, 1][5, 3])

Rule argument

Additional information

[Concretesimprules(())]