Nuprl Lemma : ext-eq-psc_wf
∀[C:SmallCategory]. ∀[X,Y:ps_context{j:l}(C)]. (X ≡ Y ∈ ℙ{[i | j']})
Proof
Definitions occuring in Statement :
ext-eq-psc: X ≡ Y,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq-psc: X ≡ Y,
ext-equal-presheaves: ext-equal-presheaves(C;F;G),
small-category: SmallCategory,
ps_context: __⊢,
cat-functor: Functor(C1;C2),
type-cat: TypeCat,
cat-comp: cat-comp(C),
op-cat: op-cat(C),
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
spreadn: spread4,
pi2: snd(t),
all: ∀x:A. B[x],
pi1: fst(t),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
ext-eq: A ≡ B
Lemmas referenced :
cat_id_tuple_lemma,
ob_pair_lemma,
arrow_pair_lemma,
ext-eq_wf,
equal_wf,
subtype_rel_dep_function,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
productEquality,
functionEquality,
cumulativity,
hypothesisEquality,
instantiate,
isectElimination,
applyEquality,
lambdaEquality_alt,
universeIsType,
independent_isectElimination,
lambdaFormation_alt,
because_Cache
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X,Y:ps\_context\{j:l\}(C)]. (X \mequiv{} Y \mmember{} \mBbbP{}\{[i | j']\})
Date html generated:
2020_05_20-PM-01_23_10
Last ObjectModification:
2020_03_31-PM-07_20_10
Theory : presheaf!models!of!type!theory
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