Nuprl Lemma : singleton-type_wf
∀[A:Type]. (singleton-type(A) ∈ Type)
Proof
Definitions occuring in Statement :
singleton-type: singleton-type(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
singleton-type: singleton-type(A),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
exists_wf,
all_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A:Type]. (singleton-type(A) \mmember{} Type)
Date html generated:
2016_05_14-PM-04_02_03
Last ObjectModification:
2015_12_26-PM-07_43_15
Theory : equipollence!!cardinality!
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