Nuprl Lemma : classical-exists1
∀[T:Type]. ∀[P:T ⟶ ℙ]. ((∃x:T. {P[x]}) ⇒ {∃x:T. P[x]})
Proof
Definitions occuring in Statement :
classical: {P},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
classical: {P},
unit: Unit
Lemmas referenced :
it_wf,
classical_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
dependent_functionElimination,
setElimination,
rename,
dependent_set_memberEquality,
axiomEquality,
natural_numberEquality,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache,
dependent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. ((\mexists{}x:T. \{P[x]\}) {}\mRightarrow{} \{\mexists{}x:T. P[x]\})
Date html generated:
2016_05_13-PM-03_16_56
Last ObjectModification:
2016_01_06-PM-05_20_41
Theory : core_2
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