Nuprl Lemma : refl-path-app
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[a:{X ⊢ _:A}]. ∀[r:{X ⊢ _:𝕀}]. (refl(a) @ r = a ∈ {X ⊢ _:A})
Proof
Definitions occuring in Statement :
cubical-refl: refl(a),
cubical-path-app: pth @ r,
interval-type: 𝕀,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
cubical-refl: refl(a),
cubical-path-app: pth @ r,
term-to-path: <>(a),
cubicalpath-app: pth @ r,
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
squash: ↓T,
true: True
Lemmas referenced :
cubical-term_wf,
interval-type_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cubical-type_wf,
cubical_set_wf,
cubical-beta,
csm-ap-type_wf,
cube-context-adjoin_wf,
cc-fst_wf,
csm-ap-term_wf,
csm_id_adjoin_fst_type_lemma,
csm_id_adjoin_fst_term_lemma,
csm-ap-id-type,
csm-ap-id-term
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
universeIsType,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
Error :memTop,
lambdaEquality_alt,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
hyp_replacement
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[a:\{X \mvdash{} \_:A\}]. \mforall{}[r:\{X \mvdash{} \_:\mBbbI{}\}]. (refl(a) @ r = a)
Date html generated:
2020_05_20-PM-03_21_58
Last ObjectModification:
2020_04_07-PM-03_30_19
Theory : cubical!type!theory
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