Nuprl Lemma : singleton-type-void-domain
∀[A:Type]. ∀[B:A ⟶ Type]. singleton-type(a:A ⟶ B[a]) supposing ¬A
Proof
Definitions occuring in Statement :
singleton-type: singleton-type(A),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
not: ¬A,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
singleton-type: singleton-type(A),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x]
Lemmas referenced :
it_wf,
all_wf,
equal_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
rename,
dependent_pairFormation,
lemma_by_obid,
hypothesis,
applyEquality,
independent_functionElimination,
cumulativity,
lambdaFormation,
functionExtensionality,
functionEquality,
isectElimination,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. singleton-type(a:A {}\mrightarrow{} B[a]) supposing \mneg{}A
Date html generated:
2016_05_14-PM-04_02_07
Last ObjectModification:
2015_12_26-PM-07_43_17
Theory : equipollence!!cardinality!
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