Nuprl Lemma : test7
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:a:A ⟶ B[a]]. ∀[x:A]. (f x ∈ B[x])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
so_lambda: λ2x.t[x]
Lemmas referenced :
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
functionIsType,
universeIsType,
applyEquality,
inhabitedIsType,
because_Cache,
universeEquality,
isect_memberFormation_alt,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
lambdaEquality_alt
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A {}\mrightarrow{} B[a]]. \mforall{}[x:A]. (f x \mmember{} B[x])
Date html generated:
2019_10_15-AM-11_36_48
Last ObjectModification:
2018_10_09-PM-00_01_06
Theory : general
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