Nuprl Lemma : compact-type-compact-type2
∀[T:Type]. (compact-type(T) ∧ T 
⇐⇒ compact-type2(T))
Proof
Definitions occuring in Statement : 
compact-type2: compact-type2(T)
, 
compact-type: compact-type(T)
, 
uall: ∀[x:A]. B[x]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
compact-type: compact-type(T)
, 
compact-type2: compact-type2(T)
, 
p-selector: p-selector(T;x;p)
, 
member: t ∈ T
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
, 
all: ∀x:A. B[x]
, 
or: P ∨ Q
, 
exists: ∃x:A. B[x]
, 
sq_exists: ∃x:{A| B[x]}
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
squash: ↓T
, 
true: True
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
guard: {T}
, 
not: ¬A
, 
false: False
, 
sq_stable: SqStable(P)
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
bfalse: ff
, 
top: Top
Lemmas referenced : 
compact-type_wf, 
compact-type2_wf, 
bool_wf, 
exists_wf, 
equal-wf-T-base, 
squash_wf, 
true_wf, 
equal_wf, 
bfalse_wf, 
iff_weakening_equal, 
btrue_neq_bfalse, 
sq_stable__all, 
sq_stable__equal, 
all_wf, 
btrue_wf, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
independent_pairFormation, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
productEquality, 
cut, 
introduction, 
extract_by_obid, 
isectElimination, 
cumulativity, 
hypothesisEquality, 
hypothesis, 
universeEquality, 
dependent_functionElimination, 
unionElimination, 
functionEquality, 
dependent_set_memberFormation, 
lambdaEquality, 
applyEquality, 
functionExtensionality, 
baseClosed, 
because_Cache, 
rename, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
natural_numberEquality, 
imageMemberEquality, 
independent_isectElimination, 
independent_functionElimination, 
voidElimination, 
setElimination, 
axiomEquality, 
equalityElimination, 
inlFormation, 
dependent_pairFormation, 
inrFormation, 
equalityUniverse, 
levelHypothesis, 
isect_memberEquality, 
voidEquality
Latex:
\mforall{}[T:Type].  (compact-type(T)  \mwedge{}  T  \mLeftarrow{}{}\mRightarrow{}  compact-type2(T))
Date html generated:
2017_10_01-AM-08_28_49
Last ObjectModification:
2017_07_26-PM-04_23_41
Theory : basic
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