Nuprl Lemma : void-dep-product
∀[S:Type]. ∀[F:S ⟶ Type]. m:S × (F m) ≡ Void supposing S ≡ Void
Proof
Definitions occuring in Statement :
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
product: x:A × B[x],
void: Void,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ
Lemmas referenced :
ext-eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
lambdaEquality,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
voidElimination,
productEquality,
voidEquality,
independent_pairEquality,
axiomEquality,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[S:Type]. \mforall{}[F:S {}\mrightarrow{} Type]. m:S \mtimes{} (F m) \mequiv{} Void supposing S \mequiv{} Void
Date html generated:
2016_05_13-PM-03_19_18
Last ObjectModification:
2015_12_26-AM-09_08_02
Theory : subtype_0
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