### Nuprl Lemma : int_seg-case

i,j:ℤ.  ∀[F,G:{i..j-} ⟶ ℙ].  ((∀k:{i..j-}. (F[k] ∨ G[k]))  ((∃k:{i..j-}. F[k]) ∨ (∀k:{i..j-}. G[k])))

Proof

Definitions occuring in Statement :  int_seg: {i..j-} uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] exists: x:A. B[x] implies:  Q or: P ∨ Q function: x:A ⟶ B[x] int:
Definitions unfolded in proof :  prop: subtype_rel: A ⊆B or: P ∨ Q so_apply: x[s] so_lambda: λ2x.t[x] member: t ∈ T implies:  Q uall: [x:A]. B[x] all: x:A. B[x]
Lemmas referenced :  istype-int subtype_rel_self int_seg_wf int-seg-case_wf
Rules used in proof :  inhabitedIsType universeEquality instantiate unionIsType functionIsType because_Cache hypothesis universeIsType applyEquality lambdaEquality_alt sqequalRule hypothesisEquality thin isectElimination sqequalHypSubstitution extract_by_obid cut introduction rename isect_memberFormation_alt lambdaFormation_alt sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}i,j:\mBbbZ{}.
\mforall{}[F,G:\{i..j\msupminus{}\}  {}\mrightarrow{}  \mBbbP{}].    ((\mforall{}k:\{i..j\msupminus{}\}.  (F[k]  \mvee{}  G[k]))  {}\mRightarrow{}  ((\mexists{}k:\{i..j\msupminus{}\}.  F[k])  \mvee{}  (\mforall{}k:\{i..j\msupminus{}\}.  G[k])))

Date html generated: 2019_10_15-AM-10_19_58
Last ObjectModification: 2019_10_02-PM-06_07_24

Theory : call!by!value_2

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