Nuprl Lemma : tupletype_cons_lemma
∀L,T:Top. (tuple-type([T / L]) ~ if null(L) then T else T × tuple-type(L) fi )
Proof
Definitions occuring in Statement :
tuple-type: tuple-type(L),
null: null(as),
cons: [a / b],
ifthenelse: if b then t else f fi ,
top: Top,
all: ∀x:A. B[x],
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
tuple-type: tuple-type(L),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
top_wf,
list_ind_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}L,T:Top. (tuple-type([T / L]) \msim{} if null(L) then T else T \mtimes{} tuple-type(L) fi )
Date html generated:
2016_05_14-PM-03_57_26
Last ObjectModification:
2015_12_26-PM-07_22_14
Theory : tuples
Home
Index