Nuprl Lemma : valueall-type-value-type
∀[A:Type]. value-type(A) supposing valueall-type(A)
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T),
value-type: value-type(T),
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,
value-type: value-type(T),
sq_stable: SqStable(P),
implies: P ⇒ Q,
all: ∀x:A. B[x],
has-value: (a)↓,
has-valueall: has-valueall(a),
prop: ℙ,
squash: ↓T
Lemmas referenced :
sq_stable__has-value,
evalall-reduce,
valueall-type-has-valueall,
equal_wf,
equal-wf-base,
base_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality,
axiomSqleEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. value-type(A) supposing valueall-type(A)
Date html generated:
2017_04_14-AM-07_35_13
Last ObjectModification:
2017_02_27-PM-03_07_58
Theory : fun_1
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