Nuprl Lemma : bl-exists-singleton
∀[T:Type]. ∀[f:T ⟶ 𝔹]. ∀[a:T]. ((∃x∈[a].f[x])_b ~ f[a])
Proof
Definitions occuring in Statement :
bl-exists: (∃x∈L.P[x])_b,
cons: [a / b],
nil: [],
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
bl-exists: (∃x∈L.P[x])_b,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
so_apply: x[s]
Lemmas referenced :
reduce_cons_lemma,
reduce_nil_lemma,
bor-bfalse,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
isectElimination,
applyEquality,
hypothesisEquality,
sqequalAxiom,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[a:T]. ((\mexists{}x\mmember{}[a].f[x])\_b \msim{} f[a])
Date html generated:
2016_05_15-PM-05_37_29
Last ObjectModification:
2015_12_27-PM-02_05_36
Theory : general
Home
Index