Nuprl Lemma : sub-presheaf-set-true
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. X | I,rho.True ≡ X
Proof
Definitions occuring in Statement :
sub-presheaf-set: X | I,rho.P[I; rho],
ext-eq-psc: X ≡ Y,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
true: True,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sub-presheaf-set: X | I,rho.P[I; rho],
ext-eq-psc: X ≡ Y,
subtype_rel: A ⊆r B,
ext-equal-presheaves: ext-equal-presheaves(C;F;G),
and: P ∧ Q,
all: ∀x:A. B[x],
ext-eq: A ≡ B,
presheaf: Presheaf(C),
ps_context: __⊢
Lemmas referenced :
presheaf-subset-true,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf,
ps_context_cumulativity2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
sqequalRule,
productElimination,
independent_pairEquality,
lambdaEquality_alt,
dependent_functionElimination,
axiomEquality,
functionIsTypeImplies,
inhabitedIsType,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. X | I,rho.True \mequiv{} X
Date html generated:
2020_05_20-PM-01_23_33
Last ObjectModification:
2020_04_01-AM-10_45_02
Theory : presheaf!models!of!type!theory
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