Nuprl Lemma : implies-wf
∀[A:ℙ]. ∀[B:⋂a:A. ℙ]. (A ⇒ B ∈ ℙ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
member: t ∈ T,
isect: ⋂x:A. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionEquality,
hypothesisEquality,
applyEquality,
lambdaEquality,
hypothesis,
rename,
isectElimination,
equalityTransitivity,
equalitySymmetry,
isectEquality,
cumulativity,
sqequalHypSubstitution,
sqequalRule,
universeEquality,
axiomEquality,
isect_memberEquality,
thin,
because_Cache
Latex:
\mforall{}[A:\mBbbP{}]. \mforall{}[B:\mcap{}a:A. \mBbbP{}]. (A {}\mRightarrow{} B \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_07_12
Last ObjectModification:
2016_01_06-PM-05_28_43
Theory : core_2
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