Nuprl Lemma : discrete-cubical-type_wf
∀[T:Type]. ∀[X:CubicalSet]. X ⊢ discr(T)
Proof
Definitions occuring in Statement :
discrete-cubical-type: discr(T)
,
cubical-type: {X ⊢ _}
,
cubical-set: CubicalSet
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
cubical-type: {X ⊢ _}
,
discrete-cubical-type: discr(T)
,
and: P ∧ Q
,
cand: A c∧ B
,
all: ∀x:A. B[x]
,
so_lambda: λ2x.t[x]
,
subtype_rel: A ⊆r B
,
uimplies: b supposing a
,
squash: ↓T
,
prop: ℙ
,
true: True
,
guard: {T}
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
implies: P
⇒ Q
,
so_apply: x[s]
Lemmas referenced :
I-cube_wf,
list_wf,
coordinate_name_wf,
name-morph_wf,
cube-set-restriction_wf,
all_wf,
equal_wf,
id-morph_wf,
subtype_rel-equal,
squash_wf,
true_wf,
cube-set-restriction-id,
iff_weakening_equal,
name-comp_wf,
cube-set-restriction-comp,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
dependent_pairEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
because_Cache,
functionEquality,
applyEquality,
functionExtensionality,
lambdaFormation,
independent_pairFormation,
productElimination,
productEquality,
independent_isectElimination,
instantiate,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
dependent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[X:CubicalSet]. X \mvdash{} discr(T)
Date html generated:
2017_10_05-AM-10_17_14
Last ObjectModification:
2017_07_28-AM-11_20_12
Theory : cubical!sets
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