Nuprl Lemma : discrete_comp_wf
∀[G:j⊢]. ∀[T:Type]. (discrete_comp(G;T) ∈ G ⊢ Compositon(discr(T)))
Proof
Definitions occuring in Statement :
discrete_comp: discrete_comp(G;T),
composition-structure: Gamma ⊢ Compositon(A),
discrete-cubical-type: discr(T),
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,
composition-structure: Gamma ⊢ Compositon(A),
squash: ↓T,
prop: ℙ,
composition-function: composition-function{j:l,i:l}(Gamma;A),
discrete-comp: discrete-comp(G;T),
comp-op-to-comp-fun: cop-to-cfun(cA),
discrete_comp: discrete_comp(G;T),
csm-composition: (comp)sigma,
composition-term: comp cA [phi ⊢→ u] a0,
subtype_rel: A ⊆r B,
csm-id-adjoin: [u],
csm-id: 1(X),
uimplies: b supposing a,
constrained-cubical-term: {Gamma ⊢ _:A[phi |⟶ t]},
cubical-term-at: u(a),
cubical-term: {X ⊢ _:A},
all: ∀x:A. B[x],
implies: P ⇒ Q,
csm-ap-type: (AF)s,
interval-1: 1(𝕀),
discrete-cubical-type: discr(T)
Lemmas referenced :
comp-op-to-comp-fun_wf2,
discrete-cubical-type_wf,
discrete-comp_wf,
istype-universe,
cubical_set_wf,
uniform-comp-function_wf,
constrained-cubical-term_wf,
csm-ap-type_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
csm-id-adjoin_wf-interval-0,
cubical-type-cumulativity2,
csm-ap-term_wf,
context-subset_wf,
csm-context-subset-subtype3,
cubical-term-eqcd,
face-type_wf,
cube_set_map_wf,
csm-discrete-cubical-type,
I_cube_wf,
fset_wf,
nat_wf,
cubical-term-equal,
istype-cubical-term,
csm-id-adjoin_wf,
interval-1_wf,
csm-context-subset-subtype2,
csm-id-adjoin_wf-interval-1,
subset-cubical-term2,
sub_cubical_set_self,
subset-cubical-term,
context-subset-is-subset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
universeEquality,
universeIsType,
applyLambdaEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_set_memberEquality_alt,
functionExtensionality,
applyEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
Error :memTop,
inhabitedIsType,
lambdaFormation_alt,
equalityIstype,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[T:Type]. (discrete\_comp(G;T) \mmember{} G \mvdash{} Compositon(discr(T)))
Date html generated:
2020_05_20-PM-05_21_39
Last ObjectModification:
2020_04_18-AM-11_56_47
Theory : cubical!type!theory
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