Nuprl Lemma : rleq_transitivity

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


Definitions occuring in Statement :  rleq: x ≤ y real: uimplies: supposing a uall: [x:A]. B[x]
Definitions unfolded in proof :  rleq: x ≤ y uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a all: x:A. B[x] implies:  Q rnonneg: rnonneg(x) le: A ≤ B and: P ∧ Q not: ¬A false: False subtype_rel: A ⊆B real: prop: iff: ⇐⇒ Q rev_implies:  Q rsub: y
Lemmas referenced :  rnonneg-radd rsub_wf less_than'_wf real_wf nat_plus_wf rnonneg_wf radd_wf rminus_wf rnonneg_functionality radd_comm req_inversion radd-assoc req_transitivity radd-ac radd_functionality req_weakening radd-rminus-assoc
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

\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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