Nuprl Lemma : pscm-id_wf
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. (1(X) ∈ psc_map{j:l}(C; X; X))
Proof
Definitions occuring in Statement :
pscm-id: 1(X),
psc_map: A ⟶ B,
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,
psc_map: A ⟶ B,
ps_context: __⊢,
subtype_rel: A ⊆r B
Lemmas referenced :
pscm-id-sq,
identity-trans_wf,
op-cat_wf,
type-cat_wf,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. (1(X) \mmember{} psc\_map\{j:l\}(C; X; X))
Date html generated:
2020_05_20-PM-01_24_15
Last ObjectModification:
2020_04_01-AM-11_00_32
Theory : presheaf!models!of!type!theory
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