### Nuprl Lemma : rleq_transitivity

`∀[x,y,z:ℝ].  (x ≤ z) supposing ((y ≤ z) and (x ≤ y))`

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` real: `ℝ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  rleq: `x ≤ y` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` all: `∀x:A. B[x]` implies: `P `` Q` rnonneg: `rnonneg(x)` le: `A ≤ B` and: `P ∧ Q` not: `¬A` false: `False` subtype_rel: `A ⊆r B` real: `ℝ` prop: `ℙ` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` rsub: `x - y`
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin isectElimination hypothesisEquality hypothesis independent_functionElimination lambdaEquality productElimination independent_pairEquality because_Cache applyEquality setElimination rename minusEquality natural_numberEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality voidElimination addLevel independent_isectElimination promote_hyp

Latex:
\mforall{}[x,y,z:\mBbbR{}].    (x  \mleq{}  z)  supposing  ((y  \mleq{}  z)  and  (x  \mleq{}  y))

Date html generated: 2016_05_18-AM-07_05_47
Last ObjectModification: 2015_12_28-AM-00_36_31

Theory : reals

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