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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