Nuprl Lemma : psc-snd_wf-presheaf-fun
∀C:SmallCategory. ∀X:ps_context{j:l}(C). ∀A,B:{X ⊢ _}. (q ∈ {X.(A ⟶ B) ⊢ _:((A)p ⟶ (B)p)})
Proof
Definitions occuring in Statement :
presheaf-fun: (A ⟶ B),
psc-snd: q,
psc-fst: p,
psc-adjoin: X.A,
presheaf-term: {X ⊢ _:A},
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
ps_context: __⊢,
all: ∀x:A. B[x],
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
squash: ↓T,
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
psc-snd_wf,
presheaf-fun_wf,
presheaf-term_wf2,
psc-adjoin_wf,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
pscm-presheaf-fun,
psc-fst_wf,
presheaf-type_wf,
ps_context_wf,
small-category-cumulativity-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
hypothesis,
applyEquality,
instantiate,
lambdaEquality_alt,
imageElimination,
sqequalRule,
dependent_functionElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
universeIsType,
inhabitedIsType
Latex:
\mforall{}C:SmallCategory. \mforall{}X:ps\_context\{j:l\}(C). \mforall{}A,B:\{X \mvdash{} \_\}. (q \mmember{} \{X.(A {}\mrightarrow{} B) \mvdash{} \_:((A)p {}\mrightarrow{} (B)p)\})
Date html generated:
2020_05_20-PM-01_30_01
Last ObjectModification:
2020_04_02-PM-06_18_24
Theory : presheaf!models!of!type!theory
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