Nuprl Lemma : is_int_wf
∀[T:Type]. ∀[x:T]. (is_int(x) ∈ 𝔹) supposing value-type(T) ∧ (T ⊆r Base)
Proof
Definitions occuring in Statement : 
is_int: is_int(x)
, 
value-type: value-type(T)
, 
bool: 𝔹
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
and: P ∧ Q
, 
member: t ∈ T
, 
base: Base
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
is_int: is_int(x)
, 
and: P ∧ Q
, 
has-value: (a)↓
, 
subtype_rel: A ⊆r B
, 
top: Top
Lemmas referenced : 
value-type-has-value, 
has-value_wf_base, 
is-exception_wf, 
btrue_wf, 
istype-top, 
istype-void, 
bfalse_wf, 
value-type_wf, 
subtype_rel_wf, 
base_wf, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
productElimination, 
thin, 
callbyvalueReduce, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
independent_isectElimination, 
hypothesis, 
isintCases, 
divergentSqle, 
because_Cache, 
baseClosed, 
applyEquality, 
isintReduceTrue, 
equalityTransitivity, 
equalitySymmetry, 
axiomSqEquality, 
Error :inhabitedIsType, 
Error :isect_memberEquality_alt, 
Error :isectIsTypeImplies, 
voidElimination, 
axiomEquality, 
Error :universeIsType, 
Error :productIsType, 
instantiate, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[x:T].  (is\_int(x)  \mmember{}  \mBbbB{})  supposing  value-type(T)  \mwedge{}  (T  \msubseteq{}r  Base)
Date html generated:
2019_06_20-AM-11_33_08
Last ObjectModification:
2019_02_07-AM-11_53_28
Theory : int_1
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