Nuprl Lemma : presheaf-lam_wf
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A,B:{X ⊢ _}]. ∀[b:{X.A ⊢ _:(B)p}].
(presheaf-lam(X;b) ∈ {X ⊢ _:(A ⟶ B)})
Proof
Definitions occuring in Statement :
presheaf-lam: presheaf-lam(X;b),
presheaf-fun: (A ⟶ B),
psc-fst: p,
psc-adjoin: X.A,
presheaf-term: {X ⊢ _:A},
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf-lam: presheaf-lam(X;b),
subtype_rel: A ⊆r B,
and: P ∧ Q
Lemmas referenced :
presheaf-fun-as-presheaf-pi,
presheaf-lambda_wf,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
pscm-ap-type_wf,
psc-adjoin_wf,
psc-fst_wf,
small-category-cumulativity-2,
presheaf-term_wf,
presheaf-type_wf,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
instantiate,
applyEquality,
because_Cache,
hypothesis,
dependent_set_memberEquality_alt,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
productIsType,
equalityIstype,
inhabitedIsType,
applyLambdaEquality,
setElimination,
rename,
productElimination,
lambdaEquality_alt,
hyp_replacement,
universeIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A,B:\{X \mvdash{} \_\}]. \mforall{}[b:\{X.A \mvdash{} \_:(B)p\}].
(presheaf-lam(X;b) \mmember{} \{X \mvdash{} \_:(A {}\mrightarrow{} B)\})
Date html generated:
2020_05_20-PM-01_30_22
Last ObjectModification:
2020_04_02-PM-03_02_15
Theory : presheaf!models!of!type!theory
Home
Index