Nuprl Lemma : exists_uni_wf
∀[T:Type]. ∀[P:T ⟶ ℙ]. (∃!x:T. P[x] ∈ ℙ)
Proof
Definitions occuring in Statement :
exists_uni: ∃!x:T. P[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists_uni: ∃!x:T. P[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
exists_wf,
and_wf,
all_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
functionEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. (\mexists{}!x:T. P[x] \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_23_14
Last ObjectModification:
2015_12_27-PM-01_05_49
Theory : general
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