Nuprl Lemma : discrete-unary_wf
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[X:j⊢]. ∀[t:{X ⊢ _:discr(A)}]. (discrete-unary(t;x.f[x]) ∈ {X ⊢ _:discr(B)})
Proof
Definitions occuring in Statement :
discrete-cubical-type: discr(T),
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
discrete-unary: discrete-unary(t;x.f[x]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
discrete-cubical-type: discr(T),
discrete-presheaf-type: discr(T)
Lemmas referenced :
discrete-unary_wf,
cube-cat_wf,
cubical-term-sq-presheaf-term
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[X:j\mvdash{}]. \mforall{}[t:\{X \mvdash{} \_:discr(A)\}].
(discrete-unary(t;x.f[x]) \mmember{} \{X \mvdash{} \_:discr(B)\})
Date html generated:
2020_05_20-PM-02_31_38
Last ObjectModification:
2020_04_03-PM-08_42_01
Theory : cubical!type!theory
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