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Proof step 614 from proof NEWPARTS-theorem (previous step)

length_of_P = # P0, Pnew = [], Pdone = [], P2 = 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) ⊦ ⟨while P2 ≠ [] do let p = P2.head in {P2 := P2.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 '}⟩ ⟨P2 := Pdone + Pnew⟩ (partitions(P2, # A) ∧ divides(P2, P0, X, A) ∧ Fok(F, P2, # A) ∧ partitionRefinement(P2, A, P4, A4, X))

User applied rule invariant right

And obtained the following new goals

Proof step 5:
length_of_P = # P0, Pnew = [], Pdone = [], P2 = 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), ∀ P1. ¬ ( P0 = P1 + P2 ∧ partitions(Pdone + P2 + Pnew, # A) ∧ divides(Pdone + Pnew, P1, X, A) ∧ Fok(F, Pdone + P2 + Pnew, # A) ∧ split(P0, A, X) ∧ # Pdone = # P1 ∧ length_of_P = # P0 ∧ partitionRefinement(Pdone + Pnew, A, P4, A4, X) ∧ samepartitions(P0, A, P4, A4)) ⊦

Rule argument

bound:# P2 inv:∃ P1. P0 = P1 + P2 ∧ partitions(Pdone + P2 + Pnew, # A) ∧ divides(Pdone + Pnew, P1, X, A) ∧ Fok(F, Pdone + P2 + Pnew, # A) ∧ split(P0, A, X) ∧ # Pdone = # P1 ∧ length_of_P = # P0 ∧ partitionRefinement(Pdone + Pnew, A, P4, A4, X) ∧ samepartitions(P0, A, P4, A4) fmapos:right 1

Additional information

[Concretesimprules(()), Extrafmas((∃ P1. P0 = P1 + P2 ∧ partitions(Pdone + P2 + Pnew, # A) ∧ divides(Pdone + Pnew, P1, X, A) ∧ Fok(F, Pdone + P2 + Pnew, # A) ∧ split(P0, A, X) ∧ # Pdone = # P1 ∧ length_of_P = # P0 ∧ partitionRefinement(Pdone + Pnew, A, P4, A4, X) ∧ samepartitions(P0, A, P4, A4) # P2 = # P2))]