Nuprl Lemma : int?_wf
∀[T:Type]. ∀[x:T]. (int?(x) ∈ {y:ℤ| y ~ x} + T) supposing value-type(T) ∧ (T ⊆r Base)
Proof
Definitions occuring in Statement :
int?: int?(x),
value-type: value-type(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
union: left + right,
int: ℤ,
base: Base,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int?: 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,
istype-sqequal,
int_subtype_base,
istype-top,
istype-void,
istype-int,
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,
Error :inlEquality_alt,
Error :dependent_set_memberEquality_alt,
Error :inhabitedIsType,
axiomSqEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
voidElimination,
Error :inrEquality_alt,
Error :setIsType,
baseApply,
closedConclusion,
axiomEquality,
Error :universeIsType,
Error :productIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. (int?(x) \mmember{} \{y:\mBbbZ{}| y \msim{} x\} + T) supposing value-type(T) \mwedge{} (T \msubseteq{}r Base)
Date html generated:
2019_06_20-AM-11_33_10
Last ObjectModification:
2019_02_07-PM-00_06_32
Theory : int_1
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