Nuprl Lemma : rv-perm-op
∀[rv,x,y:Top]. ((x y) ~ let f,g = x in let f',g' = y in <f o f', g' o g>)
Proof
Definitions occuring in Statement :
rv-permutation-group: Perm(rv),
sg-op: (x y),
compose: f o g,
uall: ∀[x:A]. B[x],
top: Top,
spread: spread def,
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
btrue: tt,
bfalse: ff,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
top: Top,
member: t ∈ T,
all: ∀x:A. B[x],
mk-s-group: mk-s-group(ss; e; i; o; sep; invsep),
permutation-s-group: Perm(rv),
sg-op: (x y),
rv-permutation-group: Perm(rv)
Lemmas referenced :
top_wf,
rec_select_update_lemma
Rules used in proof :
because_Cache,
hypothesisEquality,
isectElimination,
sqequalAxiom,
isect_memberFormation,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[rv,x,y:Top]. ((x y) \msim{} let f,g = x in let f',g' = y in <f o f', g' o g>)
Date html generated:
2016_11_08-AM-09_21_00
Last ObjectModification:
2016_11_03-AM-11_40_31
Theory : inner!product!spaces
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