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Proof step 617 from proof NEWPARTS-theorem (previous step)

P = P0, DAid(A, D), ADid(A, D), nodups(A), split(P0, A, X), partitions(P0, # A), Fok(F, P0, # A), samepartitions(P0, A, P4, A4) ⊦ ⟨let Pdone = [], Pnew = [], length_of_P = # P in {F0 := F, P1 := P; while P1 ≠ [] do let p = P1.head in {P1 := P1.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}; P1 := Pdone + Pnew}⟩ (partitions(P1, # A) ∧ divides(P1, P0, X, A) ∧ Fok(F0, P1, # A) ∧ partitionRefinement(P1, A, P4, A4, X))

Heuristic symbolic execution applied rule vardecls right

And obtained the following new goals

Proof step 616:
P = P0, DAid(A, D), ADid(A, D), nodups(A), split(P0, A, X), partitions(P0, # A), Fok(F, P0, # A), samepartitions(P0, A, P4, A4), length_of_P = # P, Pnew = [], Pdone = [] ⊦ ⟨F0 := F, P1 := P⟩ ⟨while P1 ≠ [] do let p = P1.head in {P1 := P1.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}⟩ ⟨P1 := Pdone + Pnew⟩ (partitions(P1, # A) ∧ divides(P1, P0, X, A) ∧ Fok(F0, P1, # A) ∧ partitionRefinement(P1, A, P4, A4, X))

Rule argument

Additional information

[Concretesimprules(())]