Nuprl Lemma : sp-le_transitivity
∀[x,y,z:Sierpinski].  (x ≤ y 
⇒ y ≤ z 
⇒ x ≤ z)
Proof
Definitions occuring in Statement : 
sp-le: x ≤ y
, 
Sierpinski: Sierpinski
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
sp-le: x ≤ y
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
prop: ℙ
Lemmas referenced : 
equal-wf-T-base, 
Sierpinski_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lambdaFormation, 
sqequalHypSubstitution, 
independent_functionElimination, 
thin, 
hypothesis, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
baseClosed, 
functionEquality, 
because_Cache, 
lambdaEquality, 
dependent_functionElimination, 
axiomEquality, 
isect_memberEquality
Latex:
\mforall{}[x,y,z:Sierpinski].    (x  \mleq{}  y  {}\mRightarrow{}  y  \mleq{}  z  {}\mRightarrow{}  x  \mleq{}  z)
Date html generated:
2019_10_31-AM-06_36_11
Last ObjectModification:
2017_07_28-AM-09_12_06
Theory : synthetic!topology
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