Nuprl Lemma : ifthenelse_wf
∀[b:𝔹]. ∀[A:Type]. ∀[p,q:A]. (if b then p else q fi ∈ A)
Proof
Definitions occuring in Statement :
ifthenelse: if b then t else f fi ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ifthenelse: if b then t else f fi ,
bool: 𝔹,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
unit_wf,
equal_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
unionEquality,
extract_by_obid,
lambdaFormation,
unionElimination,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
Error :inhabitedIsType,
isect_memberEquality,
Error :universeIsType,
because_Cache,
universeEquality
Latex:
\mforall{}[b:\mBbbB{}]. \mforall{}[A:Type]. \mforall{}[p,q:A]. (if b then p else q fi \mmember{} A)
Date html generated:
2019_06_20-AM-11_19_54
Last ObjectModification:
2018_09_26-AM-10_50_26
Theory : union
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