Nuprl Lemma : prob2.1
∀[U:Type]. ∀[P:U ⟶ ℙ]. ∀x:U. ((P x) ⇒ (∃x:U. (P x)))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
hypothesisEquality,
hypothesis,
applyEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[U:Type]. \mforall{}[P:U {}\mrightarrow{} \mBbbP{}]. \mforall{}x:U. ((P x) {}\mRightarrow{} (\mexists{}x:U. (P x)))
Date html generated:
2016_05_15-PM-07_43_01
Last ObjectModification:
2015_12_27-AM-11_12_50
Theory : general
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