Nuprl Lemma : p-selector_wf
∀[T:Type]. ∀[x:T]. ∀[p:T ⟶ 𝔹]. (p-selector(T;x;p) ∈ ℙ)
Proof
Definitions occuring in Statement :
p-selector: p-selector(T;x;p),
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
p-selector: p-selector(T;x;p),
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
equal_wf,
bool_wf,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[p:T {}\mrightarrow{} \mBbbB{}]. (p-selector(T;x;p) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-01_45_34
Last ObjectModification:
2015_12_27-AM-00_10_16
Theory : basic
Home
Index