Nuprl Lemma : isect-family-wf2
∀[P:𝕌{j}]. ∀[A:Type]. ∀[F:A ⟶ P ⟶ Type]. (⋂a:A. F[a] ∈ P ⟶ Type)
Proof
Definitions occuring in Statement :
isect-family: ⋂a:A. F[a],
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
isect-family: ⋂a:A. F[a],
so_apply: x[s]
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
isectEquality,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache
Latex:
\mforall{}[P:\mBbbU{}\{j\}]. \mforall{}[A:Type]. \mforall{}[F:A {}\mrightarrow{} P {}\mrightarrow{} Type]. (\mcap{}a:A. F[a] \mmember{} P {}\mrightarrow{} Type)
Date html generated:
2016_05_14-AM-06_12_06
Last ObjectModification:
2015_12_26-PM-00_06_17
Theory : co-recursion
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