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Proof step 21 from proof MAIN-theorem (conclusion)

A = A0, P = P0, ∀ p. p ∈ P → p.count = 0 ∧ okp(p, # A), DAid(A, D), ADid(A, D), nodups(A), partitions(P, # A), Fok(F, P, # A) ⊦ ⟨MAIN(X; A, D, P, F)⟩ ( perm(A0, A) ∧ partitions(P, # A) ∧ divides(P, P0, X, A) ∧ DAid(A, D) ∧ ADid(A, D) ∧ Fok(F, P, # A) ∧ partitionRefinement(P, A, P0, A0, X))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
P = P0, A = A0, DAid(A0, D), ADid(A0, D), nodups(A0), partitions(P0, # A0), Fok(F, P0, # A0), ∀ p. p ∈ P0 → p.count = 0 ∧ okp(p, # A0) ⊦ ⟨MAIN(X; A, D, P, F)⟩ ( perm(A0, A) ∧ partitions(P, # A) ∧ divides(P, P0, X, A) ∧ DAid(A, D) ∧ ADid(A, D) ∧ Fok(F, P, # A) ∧ partitionRefinement(P, A, P0, A0, X))

Rule argument

Additional information

[Concretesimprules(())]