Nuprl Lemma : valueall-type-has-valueall
∀[T:Type]. ∀[x:T]. has-valueall(x) supposing valueall-type(T)
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T),
has-valueall: has-valueall(a),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-valueall: has-valueall(a),
has-value: (a)↓,
valueall-type: valueall-type(T),
prop: ℙ
Lemmas referenced :
istype-universe,
valueall-type_wf,
sqle_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
axiomSqleEquality,
hypothesis,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
Error :isect_memberEquality_alt,
Error :universeIsType,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
pointwiseFunctionality,
independent_isectElimination,
callbyvalueReduce,
baseClosed
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. has-valueall(x) supposing valueall-type(T)
Date html generated:
2019_06_20-AM-11_20_47
Last ObjectModification:
2018_10_06-AM-09_24_51
Theory : call!by!value_1
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