Nuprl Lemma : uniform-extend-contractible
∀Gamma:j⊢. ∀A:{Gamma ⊢ _}. ∀ext:Gamma +⊢ Extension(A). {Gamma ⊢ _:Contractible(A)}
Proof
Definitions occuring in Statement :
uniform-extend: uniform-extend{i:l}(Gamma; A),
contractible-type: Contractible(A),
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Lemmas referenced :
extend-to-contraction_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
uniform-extend_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
isectElimination,
universeIsType
Latex:
\mforall{}Gamma:j\mvdash{}. \mforall{}A:\{Gamma \mvdash{} \_\}. \mforall{}ext:Gamma +\mvdash{} Extension(A). \{Gamma \mvdash{} \_:Contractible(A)\}
Date html generated:
2020_05_20-PM-05_23_21
Last ObjectModification:
2020_04_20-AM-10_13_40
Theory : cubical!type!theory
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