Nuprl Lemma : permutation-ss-eq
∀[rv,f,g,f',g':Top].  (<f, g> ≡ <f', g'> ~ ¬(fun-sep(rv;Point;f;f') ∨ fun-sep(rv;Point;g;g')))
Proof
Definitions occuring in Statement : 
permutation-ss: permutation-ss(ss)
, 
fun-sep: fun-sep(ss;A;f;g)
, 
ss-eq: x ≡ y
, 
ss-point: Point
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
not: ¬A
, 
or: P ∨ Q
, 
pair: <a, b>
, 
sqequal: s ~ t
Definitions unfolded in proof : 
member: t ∈ T
, 
ss-eq: x ≡ y
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
top_wf, 
permutation-ss-sep
Rules used in proof : 
because_Cache, 
hypothesis, 
hypothesisEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
introduction, 
cut, 
sqequalRule, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[rv,f,g,f',g':Top].    (<f,  g>  \mequiv{}  <f',  g'>  \msim{}  \mneg{}(fun-sep(rv;Point;f;f')  \mvee{}  fun-sep(rv;Point;g;g')))
Date html generated:
2016_11_08-AM-09_12_47
Last ObjectModification:
2016_11_03-AM-10_29_41
Theory : inner!product!spaces
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