Nuprl Lemma : uniform-extension-fun_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[ext:extension-fun{j:l}(Gamma; A)].
(uniform-extension-fun{j:l}(Gamma; A; ext) ∈ ℙ{[i | j'']})
Proof
Definitions occuring in Statement :
uniform-extension-fun: uniform-extension-fun{i:l}(Gamma;A;ext),
extension-fun: extension-fun{i:l}(Gamma;A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uniform-extension-fun: uniform-extension-fun{i:l}(Gamma;A;ext),
prop: ℙ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
extension-fun: extension-fun{i:l}(Gamma;A)
Lemmas referenced :
cubical_set_wf,
cube_set_map_wf,
cubical-term_wf,
face-type_wf,
thin-context-subset,
csm-ap-type_wf,
context-subset_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
csm-context-subset-subtype2,
equal_wf,
constrained-cubical-term_wf,
csm-ap-term_wf,
csm-face-type,
context-subset-map,
csm-constrained-cubical-term,
extension-fun_wf,
cubical-type_wf,
csm-ap-comp-type-sq,
csm-comp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalRule,
functionEquality,
thin,
instantiate,
introduction,
extract_by_obid,
hypothesis,
because_Cache,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
lambdaEquality_alt,
cumulativity,
universeIsType,
universeEquality,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
hyp_replacement
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[ext:extension-fun\{j:l\}(Gamma; A)].
(uniform-extension-fun\{j:l\}(Gamma; A; ext) \mmember{} \mBbbP{}\{[i | j'']\})
Date html generated:
2020_05_20-PM-05_22_08
Last ObjectModification:
2020_04_17-AM-09_22_24
Theory : cubical!type!theory
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