Nuprl Lemma : discrete-fun_wf
∀[A,B:Type]. ∀[X:j⊢]. ∀[f:{X ⊢ _:(discr(A) ⟶ discr(B))}]. (discrete-fun(f) ∈ {X ⊢ _:discr(A ⟶ B)})
Proof
Definitions occuring in Statement :
discrete-fun: discrete-fun(f),
discrete-cubical-type: discr(T),
cubical-fun: (A ⟶ B),
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
discrete-fun: discrete-fun(f),
cubical-term: {X ⊢ _:A},
discrete-cubical-type: discr(T),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
cubical-fun: (A ⟶ B),
cubical-fun-family: cubical-fun-family(X; A; B; I; a),
squash: ↓T,
prop: ℙ,
true: True,
implies: P ⇒ Q,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
cubical-term_wf,
cubical-fun_wf,
discrete-cubical-type_wf,
cubical_set_wf,
istype-universe,
cubical_type_at_pair_lemma,
nh-id_wf,
I_cube_wf,
fset_wf,
nat_wf,
cubical_type_ap_morph_pair_lemma,
names-hom_wf,
equal_wf,
squash_wf,
true_wf,
nh-id-left,
subtype_rel_self,
iff_weakening_equal,
nh-id-right,
istype-cubical-type-at,
cube-set-restriction_wf,
cubical-type-ap-morph_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
thin,
instantiate,
extract_by_obid,
isectElimination,
hypothesisEquality,
cumulativity,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeEquality,
dependent_set_memberEquality_alt,
dependent_functionElimination,
Error :memTop,
lambdaEquality_alt,
applyEquality,
because_Cache,
setElimination,
rename,
lambdaFormation_alt,
functionExtensionality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
hyp_replacement,
natural_numberEquality,
equalityIstype,
independent_functionElimination,
independent_isectElimination,
productElimination,
functionIsType,
functionEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[X:j\mvdash{}]. \mforall{}[f:\{X \mvdash{} \_:(discr(A) {}\mrightarrow{} discr(B))\}].
(discrete-fun(f) \mmember{} \{X \mvdash{} \_:discr(A {}\mrightarrow{} B)\})
Date html generated:
2020_05_20-PM-03_37_59
Last ObjectModification:
2020_04_07-PM-04_28_44
Theory : cubical!type!theory
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