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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