Nuprl Lemma : predicate-not_wf

∀[T:Type]. ∀[A:T ⟶ Type].  (¬(A) ∈ T ⟶ ℙ)


Proof




Definitions occuring in Statement :  predicate-not: ¬(A),  uall: ∀[x:A]. B[x],  prop: ℙ,  member: t ∈ T,  function: x:A ⟶ B[x],  universe: Type
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  predicate-not: ¬(A),  subtype_rel: A ⊆r B,  prop: ℙ
Lemmas referenced :  not_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation,  introduction,  cut,  sqequalRule,  lambdaEquality,  lemma_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  applyEquality,  hypothesisEquality,  hypothesis,  because_Cache,  axiomEquality,  equalityTransitivity,  equalitySymmetry,  functionEquality,  cumulativity,  universeEquality,  isect_memberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[A:T  {}\mrightarrow{}  Type].    (\mneg{}(A)  \mmember{}  T  {}\mrightarrow{}  \mBbbP{})



Date html generated: 2016_05_14-PM-04_08_54
Last ObjectModification: 2015_12_26-PM-07_54_51

Theory : fan-theorem


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