Nuprl Lemma : rleq_functionality_wrt_implies

[a,b,c,d:ℝ].  ({a ≤ supposing b ≤ c}) supposing ((c ≤ d) and (b ≥ a))


Definitions occuring in Statement :  rge: x ≥ y rleq: x ≤ y real: uimplies: supposing a uall: [x:A]. B[x] guard: {T}
Definitions unfolded in proof :  guard: {T} uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a rge: x ≥ y rleq: x ≤ y rnonneg: rnonneg(x) all: x:A. B[x] le: A ≤ B and: P ∧ Q not: ¬A implies:  Q false: False subtype_rel: A ⊆B real: prop:
Lemmas referenced :  rleq_transitivity less_than'_wf rsub_wf real_wf nat_plus_wf rleq_wf rge_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut sqequalHypSubstitution hypothesis lemma_by_obid isectElimination thin hypothesisEquality independent_isectElimination lambdaEquality dependent_functionElimination productElimination independent_pairEquality because_Cache applyEquality setElimination rename minusEquality natural_numberEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality voidElimination

\mforall{}[a,b,c,d:\mBbbR{}].    (\{a  \mleq{}  d  supposing  b  \mleq{}  c\})  supposing  ((c  \mleq{}  d)  and  (b  \mgeq{}  a))

Date html generated: 2016_05_18-AM-07_06_07
Last ObjectModification: 2015_12_28-AM-00_36_44

Theory : reals

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