Nuprl Lemma : cubical-refl_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[a:{X ⊢ _:A}]. (refl(a) ∈ {X ⊢ _:(Path_A a a)})
Proof
Definitions occuring in Statement :
cubical-refl: refl(a),
path-type: (Path_A a b),
cubical-term: {X ⊢ _:A},
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-refl: refl(a),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
squash: ↓T,
prop: ℙ,
true: True
Lemmas referenced :
term-to-path_wf,
csm-ap-term_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
cc-fst_wf,
cubical-term_wf,
cubical-type-cumulativity2,
cubical-type_wf,
cubical_set_wf,
squash_wf,
true_wf,
path-type_wf,
csm_id_adjoin_fst_term_lemma,
csm-ap-id-term
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
instantiate,
applyEquality,
hypothesis,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaEquality_alt,
hyp_replacement,
universeIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
imageElimination,
Error :memTop,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[a:\{X \mvdash{} \_:A\}]. (refl(a) \mmember{} \{X \mvdash{} \_:(Path\_A a a)\})
Date html generated:
2020_05_20-PM-03_20_58
Last ObjectModification:
2020_04_06-PM-06_37_54
Theory : cubical!type!theory
Home
Index