Nuprl Lemma : value-type_functionality
∀[T,T':Type].  value-type(T) 
⇐⇒ value-type(T') supposing T ≡ T'
Proof
Definitions occuring in Statement : 
value-type: value-type(T)
, 
ext-eq: A ≡ B
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
iff: P 
⇐⇒ Q
, 
universe: Type
Definitions unfolded in proof : 
value-type: value-type(T)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
has-value: (a)↓
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
ext-eq_inversion, 
subtype_rel_weakening, 
equal-wf-base, 
base_wf, 
uall_wf, 
isect_wf, 
has-value_wf_base, 
ext-eq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
independent_pairFormation, 
lambdaFormation, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
applyEquality, 
lemma_by_obid, 
axiomSqleEquality, 
because_Cache, 
isect_memberEquality, 
lambdaEquality, 
productElimination, 
independent_pairEquality, 
dependent_functionElimination, 
universeEquality
Latex:
\mforall{}[T,T':Type].    value-type(T)  \mLeftarrow{}{}\mRightarrow{}  value-type(T')  supposing  T  \mequiv{}  T'
Date html generated:
2016_05_13-PM-03_24_16
Last ObjectModification:
2015_12_26-AM-09_30_25
Theory : call!by!value_1
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