Nuprl Lemma : lifted-rel_wf
∀[A,B:Type]. ∀[R:A ⟶ A ⟶ ℙ]. (lifted-rel(R) ∈ (A + B) ⟶ (A + B) ⟶ ℙ)
Proof
Definitions occuring in Statement :
lifted-rel: lifted-rel(R),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lifted-rel: lifted-rel(R),
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
implies: P ⇒ Q,
prop: ℙ,
bfalse: ff,
and: P ∧ Q,
false: False
Lemmas referenced :
and_wf,
true_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
unionElimination,
thin,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
functionEquality,
applyEquality,
hypothesisEquality,
productEquality,
voidElimination,
because_Cache,
unionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (lifted-rel(R) \mmember{} (A + B) {}\mrightarrow{} (A + B) {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_15-PM-06_35_23
Last ObjectModification:
2015_12_27-AM-11_55_46
Theory : general
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