Nuprl Lemma : comp-op_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢j _}]. (comp-op(Gamma;A) ∈ 𝕌{[i | j]'})
Proof
Definitions occuring in Statement :
comp-op: comp-op(Gamma;A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
comp-op: comp-op(Gamma;A),
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
fset_wf,
nat_wf,
not_wf,
fset-member_wf,
int-deq_wf,
istype-nat,
I_cube_wf,
add-name_wf,
face-presheaf_wf2,
cubical-term_wf,
cubical-subset_wf,
cube-set-restriction_wf,
nc-s_wf,
f-subset-add-name,
csm-ap-type_wf,
cubical_set_cumulativity-i-j,
csm-comp_wf,
formal-cube_wf1,
subset-iota_wf,
context-map_wf,
cubical-path-0_wf,
istype-void,
cubical-path-1_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality_alt,
cumulativity,
hypothesisEquality,
universeIsType,
universeEquality,
setEquality,
because_Cache,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
lambdaFormation_alt,
setElimination,
rename,
instantiate,
independent_isectElimination,
dependent_functionElimination,
dependent_set_memberEquality_alt,
functionIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{}j \_\}]. (comp-op(Gamma;A) \mmember{} \mBbbU{}\{[i | j]'\})
Date html generated:
2020_05_20-PM-03_48_40
Last ObjectModification:
2020_04_09-AM-11_17_25
Theory : cubical!type!theory
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