Nuprl Lemma : cocons_wf
∀[A:Type]. ∀[a:A]. ∀[L:co-list-islist(A)]. (cocons(a;L) ∈ co-list-islist(A))
Proof
Definitions occuring in Statement :
cocons: cocons(a;L),
co-list-islist: co-list-islist(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
co-list-islist: co-list-islist(T),
cocons: cocons(a;L),
subtype_rel: A ⊆r B,
is-list: is-list(t),
pi2: snd(t),
uimplies: b supposing a,
bool: 𝔹,
prop: ℙ,
ext-eq: A ≡ B,
and: P ∧ Q
Lemmas referenced :
colist-ext,
subtype_rel_b-union-right,
unit_wf2,
colist_wf,
istype-universe,
has-value_wf-partial,
bool_wf,
union-value-type,
is-list_wf,
co-list-islist_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
dependent_set_memberEquality_alt,
independent_pairEquality,
applyEquality,
productEquality,
sqequalRule,
independent_isectElimination,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality,
productElimination
Latex:
\mforall{}[A:Type]. \mforall{}[a:A]. \mforall{}[L:co-list-islist(A)]. (cocons(a;L) \mmember{} co-list-islist(A))
Date html generated:
2019_10_16-AM-11_38_50
Last ObjectModification:
2019_06_26-PM-04_07_01
Theory : eval!all
Home
Index