Nuprl Lemma : prob2.2
∀[U:Type]. ∀[P,Q:U ⟶ ℙ]. ((∃x:U. ((P x) ∨ (Q x))) ⇒ ((∃x:U. (P x)) ∨ (∃x:U. (Q x))))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
exists: ∃x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
cumulativity,
universeEquality,
inlFormation,
dependent_pairFormation,
inrFormation
Latex:
\mforall{}[U:Type]. \mforall{}[P,Q:U {}\mrightarrow{} \mBbbP{}]. ((\mexists{}x:U. ((P x) \mvee{} (Q x))) {}\mRightarrow{} ((\mexists{}x:U. (P x)) \mvee{} (\mexists{}x:U. (Q x))))
Date html generated:
2016_05_15-PM-07_43_18
Last ObjectModification:
2015_12_27-AM-11_12_01
Theory : general
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