### Nuprl Lemma : rminus-reverses-rleq

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

Proof

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

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

Date html generated: 2016_05_18-AM-07_07_24
Last ObjectModification: 2015_12_28-AM-00_38_51

Theory : reals

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