Nuprl Lemma : contractible-uniform-extend
∀Gamma:j⊢. ∀A:{Gamma ⊢ _}. ∀cA:Gamma ⊢ Compositon(A). ∀ctr:{Gamma ⊢ _:Contractible(A)}. Gamma ⊢ Extension(A)
Proof
Definitions occuring in Statement :
uniform-extend: uniform-extend{i:l}(Gamma; A),
composition-structure: Gamma ⊢ Compositon(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,
uall: ∀[x:A]. B[x]
Lemmas referenced :
contraction-to-extend_wf,
istype-cubical-term,
contractible-type_wf,
composition-structure_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate
Latex:
\mforall{}Gamma:j\mvdash{}. \mforall{}A:\{Gamma \mvdash{} \_\}. \mforall{}cA:Gamma \mvdash{} Compositon(A). \mforall{}ctr:\{Gamma \mvdash{} \_:Contractible(A)\}.
Gamma \mvdash{} Extension(A)
Date html generated:
2020_05_20-PM-05_23_36
Last ObjectModification:
2020_04_19-PM-01_51_55
Theory : cubical!type!theory
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