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Proof step 5 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), ∀ 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)) ⊦

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

[Concretesimprules((Csimpnamedseq(empty-divides,,, ⊦ divides([], P1, X, A1)) Csimpnamedseq(list,partition,app, ⊦ P + [] = P) Csimpnamedseq(list,partition,Nil, ⊦ [] + P = P) Csimpnamedseq(list,partition,a, ⊦ (P + P0) + P1 = P + P0 + P1) Csimpnamedseq(list,partition,app-05, ⊦ P = P0 + P ↔ P0 = [])))]