Nuprl Lemma : pi1_wf_top
∀[T:Type]. ∀[p:T × Top]. (fst(p) ∈ T)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
pi1_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[p:T \mtimes{} Top]. (fst(p) \mmember{} T)
Date html generated:
2016_05_15-PM-03_24_18
Last ObjectModification:
2015_12_27-PM-01_05_54
Theory : general
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