Nuprl Lemma : ss-fun-sep
∀[X,Y,f,g:Top]. (f # g ~ ∃a:Point(X). f a # g a)
Proof
Definitions occuring in Statement :
ss-fun: X ⟶ Y,
ss-sep: x # y,
ss-point: Point(ss),
uall: ∀[x:A]. B[x],
top: Top,
exists: ∃x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
exists: ∃x:A. B[x],
fun-sep: fun-sep(ss;A;f;g),
fun-ss: A ⟶ ss,
btrue: tt,
bfalse: ff,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-update: r[x := v],
mk-ss: Point=P #=Sep symm=Sym cotrans=C,
set-ss: {x:ss | P[x]},
ss-fun: X ⟶ Y,
record-select: r.x,
ss-sep: x # y,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf
Rules used in proof :
because_Cache,
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
sqequalHypSubstitution,
extract_by_obid,
sqequalAxiom,
hypothesis,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y,f,g:Top]. (f \# g \msim{} \mexists{}a:Point(X). f a \# g a)
Date html generated:
2018_07_29-AM-10_11_42
Last ObjectModification:
2018_07_04-PM-00_01_40
Theory : constructive!algebra
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