Nuprl Lemma : psc-adjoin-I_set
∀[Gamma,A,I:Top]. (Gamma.A(I) ~ alpha:Gamma(I) × A(alpha))
Proof
Definitions occuring in Statement :
psc-adjoin: X.A,
presheaf-type-at: A(a),
I_set: A(I),
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
I_set: A(I),
psc-adjoin: X.A,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
ob_pair_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[Gamma,A,I:Top]. (Gamma.A(I) \msim{} alpha:Gamma(I) \mtimes{} A(alpha))
Date html generated:
2018_05_22-PM-10_05_04
Last ObjectModification:
2018_05_20-PM-09_49_52
Theory : presheaf!models!of!type!theory
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