Nuprl Lemma : ps-sigma-unelim-p
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. ∀[B:{X.A ⊢ _}].
(p o SigmaUnElim = p o p ∈ psc_map{[i | j]:l}(C; X.A.B; X))
Proof
Definitions occuring in Statement :
sigma-unelim-pscm: SigmaUnElim,
presheaf-sigma: Σ A B,
psc-fst: p,
psc-adjoin: X.A,
presheaf-type: {X ⊢ _},
pscm-comp: G o F,
psc_map: A ⟶ B,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
psc-adjoin: X.A,
all: ∀x:A. B[x],
psc-fst: p,
pscm-comp: G o F,
sigma-unelim-pscm: SigmaUnElim,
compose: f o g,
pi1: fst(t),
psc-adjoin-set: (v;u)
Lemmas referenced :
pscm-equal,
psc-adjoin_wf,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
pscm-comp_wf,
presheaf-sigma_wf,
sigma-unelim-pscm_wf,
psc-fst_wf,
psc-map-subtype,
I_set_pair_redex_lemma,
I_set_wf,
cat-ob_wf,
presheaf-type_wf,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
independent_isectElimination,
functionExtensionality,
dependent_functionElimination,
Error :memTop,
productElimination,
universeIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[B:\{X.A \mvdash{} \_\}].
(p o SigmaUnElim = p o p)
Date html generated:
2020_05_20-PM-01_32_57
Last ObjectModification:
2020_04_02-PM-06_45_59
Theory : presheaf!models!of!type!theory
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