Nuprl Lemma : set-ss-eq
∀[ss,P,x,y:Top]. (x ≡ y ~ x ≡ y)
Proof
Definitions occuring in Statement :
set-ss: set-ss(ss;x.P[x]),
ss-eq: x ≡ y,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
so_apply: x[s],
top: Top,
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
ss-eq: x ≡ y
Lemmas referenced :
top_wf,
set-ss-sep
Rules used in proof :
because_Cache,
sqequalAxiom,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[ss,P,x,y:Top]. (x \mequiv{} y \msim{} x \mequiv{} y)
Date html generated:
2016_11_08-AM-09_12_11
Last ObjectModification:
2016_11_03-AM-00_05_02
Theory : inner!product!spaces
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