Nuprl Lemma : apply-ifthenelse
∀[T,U:Type]. ∀[f:T ⟶ U]. ∀[b:𝔹]. ∀[x,y:T]. (f[if b then x else y fi ] ~ if b then f[x] else f[y] fi )
Proof
Definitions occuring in Statement :
ifthenelse: if b then t else f fi ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
bool: 𝔹,
ifthenelse: if b then t else f fi ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
bool_wf
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
unionElimination,
thin,
sqequalRule,
hypothesisEquality,
because_Cache,
cut,
lemma_by_obid,
hypothesis,
functionEquality,
universeEquality,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality,
isectElimination
Latex:
\mforall{}[T,U:Type]. \mforall{}[f:T {}\mrightarrow{} U]. \mforall{}[b:\mBbbB{}]. \mforall{}[x,y:T].
(f[if b then x else y fi ] \msim{} if b then f[x] else f[y] fi )
Date html generated:
2016_05_13-PM-04_01_23
Last ObjectModification:
2015_12_26-AM-10_49_03
Theory : bool_1
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