Nuprl Lemma : lift-predicate_wf
∀[A:Type]. ∀[P:A ⟶ ℙ]. P? ∈ bar(A) ⟶ ℙ supposing value-type(A)
Proof
Definitions occuring in Statement :
lift-predicate: P?,
bar: bar(T),
value-type: value-type(T),
uimplies: b supposing a,
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,
uimplies: b supposing a,
lift-predicate: P?,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
bar: bar(T)
Lemmas referenced :
termination,
value-type_wf,
bar_wf,
has-value_wf-bar
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
independent_isectElimination,
hypothesis,
applyEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. P? \mmember{} bar(A) {}\mrightarrow{} \mBbbP{} supposing value-type(A)
Date html generated:
2016_05_15-PM-10_04_26
Last ObjectModification:
2016_01_05-PM-06_50_55
Theory : bar!type
Home
Index