Nuprl Lemma : co-cons_one_one
∀[T:Type]. ∀[a,a':T]. ∀[b,b':colist(T)]. uiff([a / b] = [a' / b'] ∈ colist(T);{(a = a' ∈ T) ∧ (b = b' ∈ colist(T))})
Proof
Definitions occuring in Statement :
co-cons: [x / L],
colist: colist(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
guard: {T},
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
true: True,
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: (),
false: False,
co-cons: [x / L],
hd: hd(l),
pi1: fst(t)
Lemmas referenced :
co-cons_wf,
colist-ext,
isaxiom_wf_listunion,
colist_wf,
subtype_rel_b-union-left,
unit_wf2,
axiom-listunion,
subtype_rel_b-union-right,
non-axiom-listunion,
reduce_hd_cons_lemma,
istype-void,
co-cons-not-co-nil,
reduce_tl_nil_lemma,
reduce_tl_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
hypothesis,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
axiomEquality,
Error :equalityIstype,
Error :inhabitedIsType,
hypothesisEquality,
extract_by_obid,
isectElimination,
applyEquality,
Error :lambdaEquality_alt,
imageElimination,
because_Cache,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
Error :productIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :dependent_set_memberEquality_alt,
equalityTransitivity,
applyLambdaEquality,
setElimination,
rename,
promote_hyp,
hypothesis_subsumption,
Error :lambdaFormation_alt,
unionElimination,
equalityElimination,
productEquality,
independent_isectElimination,
dependent_functionElimination,
voidElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[a,a':T]. \mforall{}[b,b':colist(T)]. uiff([a / b] = [a' / b'];\{(a = a') \mwedge{} (b = b')\})
Date html generated:
2019_06_20-PM-00_41_56
Last ObjectModification:
2019_01_02-PM-05_25_05
Theory : list_0
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