Nuprl Lemma : co-cons-not-co-nil
∀[T:Type]. ∀[a:T]. ∀[b:colist(T)]. uiff([a / b] = () ∈ colist(T);False)
Proof
Definitions occuring in Statement :
co-cons: [x / L],
co-nil: (),
colist: colist(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
false: False,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
false: False,
ext-eq: A ≡ B,
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],
top: Top,
co-nil: (),
co-cons: [x / L],
not: ¬A
Lemmas referenced :
colist-ext,
isaxiom_wf_listunion,
colist_wf,
subtype_rel_b-union-left,
unit_wf2,
axiom-listunion,
null_nil_lemma,
btrue_wf,
subtype_rel_b-union-right,
non-axiom-listunion,
null_cons_lemma,
istype-void,
bfalse_wf,
co-cons_wf,
co-nil_wf,
istype-universe,
btrue_neq_bfalse
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
applyLambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
promote_hyp,
productElimination,
hypothesis_subsumption,
hypothesis,
applyEquality,
sqequalRule,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
equalityElimination,
productEquality,
independent_isectElimination,
rename,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
because_Cache,
independent_pairEquality,
Error :isectIsTypeImplies,
axiomEquality,
Error :universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[b:colist(T)]. uiff([a / b] = ();False)
Date html generated:
2019_06_20-PM-00_41_50
Last ObjectModification:
2019_01_02-PM-05_22_38
Theory : list_0
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