Nuprl Lemma : pscm-ap-presheaf-lambda
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. ∀[B:{X.A ⊢ _}]. ∀[b:{X.A ⊢ _:B}]. ∀[H:ps_context{j:l}(C)].
∀[s:psc_map{j:l}(C; H; X)].
(((λb))s = (λ(b)s+) ∈ {H ⊢ _:(ΠA B)s})
Proof
Definitions occuring in Statement :
presheaf-lambda: (λb),
presheaf-pi: ΠA B,
pscm+: tau+,
psc-adjoin: X.A,
pscm-ap-term: (t)s,
presheaf-term: {X ⊢ _:A},
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
psc_map: A ⟶ B,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
small-category: SmallCategory
Lemmas referenced :
pscm-presheaf-lambda
Rules used in proof :
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[B:\{X.A \mvdash{} \_\}]. \mforall{}[b:\{X.A \mvdash{} \_:B\}].
\mforall{}[H:ps\_context\{j:l\}(C)]. \mforall{}[s:psc\_map\{j:l\}(C; H; X)].
(((\mlambda{}b))s = (\mlambda{}(b)s+))
Date html generated:
2020_05_20-PM-01_33_23
Last ObjectModification:
2020_04_02-PM-06_31_04
Theory : presheaf!models!of!type!theory
Home
Index