Nuprl Lemma : is-list-fun_wf
∀[T:Type]. (is-list-fun() ∈ (colist(T) ⟶ partial(𝔹)) ⟶ colist(T) ⟶ partial(𝔹))
Proof
Definitions occuring in Statement :
is-list-fun: is-list-fun(),
colist: colist(T),
partial: partial(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-list-fun: is-list-fun(),
has-value: (a)↓,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
nil: [],
bfalse: ff,
cons: [a / b],
pi2: snd(t),
prop: ℙ
Lemmas referenced :
value-type-has-value,
colist_wf,
colist-value-type,
co-list-has-value,
co-list-subtype,
b-union_wf,
unit_wf2,
isaxiom_wf_listunion,
bool_wf,
subtype_rel_b-union-left,
axiom-listunion,
btrue_wf,
inclusion-partial,
union-value-type,
subtype_rel_b-union-right,
non-axiom-listunion,
equal_wf,
partial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
independent_isectElimination,
applyEquality,
productEquality,
lambdaFormation,
unionElimination,
equalityElimination,
hypothesis_subsumption,
because_Cache,
productElimination,
rename,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. (is-list-fun() \mmember{} (colist(T) {}\mrightarrow{} partial(\mBbbB{})) {}\mrightarrow{} colist(T) {}\mrightarrow{} partial(\mBbbB{}))
Date html generated:
2018_05_21-PM-10_19_46
Last ObjectModification:
2017_07_26-PM-06_37_10
Theory : eval!all
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