Nuprl Lemma : ite_wf
∀[b:𝔹]. ∀[T:Type]. ∀[x:T supposing ↑b]. ∀[y:T supposing ¬↑b]. (ite(b;x;y) ∈ T)
Proof
Definitions occuring in Statement :
ite: ite(b;x;y),
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
ite: ite(b;x;y),
bool: 𝔹,
assert: ↑b,
ifthenelse: if b then t else f fi ,
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
true: True,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
not_wf,
assert_wf,
bool_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalHypSubstitution,
unionElimination,
thin,
sqequalRule,
isectEquality,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
because_Cache,
universeEquality,
isect_memberFormation,
introduction,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
independent_isectElimination,
natural_numberEquality,
lambdaEquality,
voidElimination,
lambdaFormation
Latex:
\mforall{}[b:\mBbbB{}]. \mforall{}[T:Type]. \mforall{}[x:T supposing \muparrow{}b]. \mforall{}[y:T supposing \mneg{}\muparrow{}b]. (ite(b;x;y) \mmember{} T)
Date html generated:
2016_05_15-PM-03_26_22
Last ObjectModification:
2015_12_27-PM-01_07_25
Theory : general
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