Nuprl Lemma : cubical-identity_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[a,b:{X ⊢ _:A}].  X ⊢ (Id_A a b)
Proof
Definitions occuring in Statement : 
cubical-identity: (Id_A a b)
, 
cubical-term: {X ⊢ _:AF}
, 
cubical-type: {X ⊢ _}
, 
cubical-set: CubicalSet
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
cubical-type: {X ⊢ _}
, 
cubical-identity: (Id_A a b)
, 
all: ∀x:A. B[x]
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
squash: ↓T
, 
prop: ℙ
, 
true: True
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
cubical-path_wf, 
I-cube_wf, 
list_wf, 
coordinate_name_wf, 
I-path-morph_wf2, 
name-morph_wf, 
cube-set-restriction_wf, 
equal_wf, 
squash_wf, 
true_wf, 
I-path-morph-id, 
iff_weakening_equal, 
I-path-morph-comp, 
all_wf, 
id-morph_wf, 
subtype_rel-equal, 
cube-set-restriction-id, 
name-comp_wf, 
cube-set-restriction-comp, 
cubical-term_wf, 
cubical-type_wf, 
cubical-set_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
dependent_set_memberEquality, 
dependent_pairEquality, 
lambdaEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
sqequalRule, 
dependent_functionElimination, 
because_Cache, 
functionEquality, 
applyEquality, 
functionExtensionality, 
lambdaFormation, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
independent_isectElimination, 
productElimination, 
independent_functionElimination, 
independent_pairFormation, 
productEquality, 
instantiate, 
axiomEquality, 
isect_memberEquality
Latex:
\mforall{}[X:CubicalSet].  \mforall{}[A:\{X  \mvdash{}  \_\}].  \mforall{}[a,b:\{X  \mvdash{}  \_:A\}].    X  \mvdash{}  (Id\_A  a  b)
Date html generated:
2017_10_05-PM-03_56_05
Last ObjectModification:
2017_07_28-AM-11_28_35
Theory : cubical!sets
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