Nuprl Lemma : truncate_wf
∀[X:Type]. ∀[x:X]. (|x| ∈ ⇃(X))
Proof
Definitions occuring in Statement :
truncate: |x|,
quotient: x,y:A//B[x; y],
uall: ∀[x:A]. B[x],
true: True,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
truncate: |x|,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
subtype_quotient,
true_wf,
equiv_rel_true,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
hypothesisEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :lambdaEquality_alt,
hypothesis,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[x:X]. (|x| \mmember{} \00D9(X))
Date html generated:
2019_06_20-PM-00_32_48
Last ObjectModification:
2018_11_16-AM-11_46_33
Theory : quot_1
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