Nuprl Lemma : presheaf-pi-intro
∀C:SmallCategory. ∀G:ps_context{j:l}(C). ∀A:{G ⊢ _}. ∀B:{G.A ⊢ _}. ({G.A ⊢ _:B} ⇒ {G ⊢ _:ΠA B})
Proof
Definitions occuring in Statement :
presheaf-pi: ΠA B,
psc-adjoin: X.A,
presheaf-term: {X ⊢ _:A},
presheaf-type: {X ⊢ _},
ps_context: __⊢,
all: ∀x:A. B[x],
implies: P ⇒ Q,
small-category: SmallCategory
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
presheaf-lambda_wf,
presheaf-term_wf2,
psc-adjoin_wf,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
presheaf-type_wf,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
rename,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate,
applyEquality,
because_Cache,
sqequalRule
Latex:
\mforall{}C:SmallCategory. \mforall{}G:ps\_context\{j:l\}(C). \mforall{}A:\{G \mvdash{} \_\}. \mforall{}B:\{G.A \mvdash{} \_\}. (\{G.A \mvdash{} \_:B\} {}\mRightarrow{} \{G \mvdash{} \_:\mPi{}A B\})
Date html generated:
2020_05_20-PM-01_35_31
Last ObjectModification:
2020_04_02-PM-06_35_33
Theory : presheaf!models!of!type!theory
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