Nuprl Lemma : set-ss-sep
∀[ss,P,x,y:Top]. (x # y ~ x # y)
Proof
Definitions occuring in Statement :
set-ss: set-ss(ss;x.P[x]),
ss-sep: x # y,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
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-ss: mk-ss,
set-ss: set-ss(ss;x.P[x]),
ss-sep: x # y
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{}[ss,P,x,y:Top]. (x \# y \msim{} x \# y)
Date html generated:
2016_11_08-AM-09_12_09
Last ObjectModification:
2016_11_03-AM-00_04_15
Theory : inner!product!spaces
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