Nuprl Lemma : apply-ifthenelse-pi1
∀[T1,U1,T2,U2:Type]. ∀[x:T1 × U1]. ∀[y:T2 × U2]. ∀[b:𝔹].
(fst(if b then x else y fi ) ~ if b then fst(x) else fst(y) fi )
Proof
Definitions occuring in Statement :
ifthenelse: if b then t else f fi ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
pi1: fst(t),
product: 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,
cut,
lemma_by_obid,
hypothesis,
because_Cache,
productEquality,
hypothesisEquality,
universeEquality,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality,
isectElimination
Latex:
\mforall{}[T1,U1,T2,U2:Type]. \mforall{}[x:T1 \mtimes{} U1]. \mforall{}[y:T2 \mtimes{} U2]. \mforall{}[b:\mBbbB{}].
(fst(if b then x else y fi ) \msim{} if b then fst(x) else fst(y) fi )
Date html generated:
2016_05_13-PM-04_01_29
Last ObjectModification:
2015_12_26-AM-10_48_54
Theory : bool_1
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