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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