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Proof step 48 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] ⊦ ⟨NEWPARTS(; P, F)⟩ (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 nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 47:
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])

Rule argument

pos:right 1

Additional information

[Concretesimprules((Csimpdecl(NEWPARTS(; P, F) {let Pdone = [], Pnew = [], length_of_P = # P in {while P ≠ [] do let p = P.head in {P := P.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), F := F [ p.first + p.count, p.last, length_of_P + # Pnew ] else Pdone := Pdone + p}; P := Pdone + Pnew} })))]