Nuprl Lemma : apply-ifthenelse2
∀[T1,U1,T2,U2:Type]. ∀[x:T1]. ∀[y:T2]. ∀[b:𝔹]. ∀[f:if b then T1 ⟶ U1 else T2 ⟶ U2 fi ].
(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 :
ifthenelse_wf,
bool_wf
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
unionElimination,
thin,
sqequalRule,
cut,
instantiate,
lemma_by_obid,
isectElimination,
hypothesisEquality,
universeEquality,
functionEquality,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[T1,U1,T2,U2:Type]. \mforall{}[x:T1]. \mforall{}[y:T2]. \mforall{}[b:\mBbbB{}]. \mforall{}[f:if b then T1 {}\mrightarrow{} U1 else T2 {}\mrightarrow{} U2 fi ].
(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_26
Last ObjectModification:
2015_12_26-AM-10_49_08
Theory : bool_1
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