Nuprl Lemma : rleq_functionality

[x1,x2,y1,y2:ℝ].  (uiff(x1 ≤ y1;x2 ≤ y2)) supposing ((y1 y2) and (x1 x2))


Definitions occuring in Statement :  rleq: x ≤ y req: y real: uiff: uiff(P;Q) uimplies: supposing a uall: [x:A]. B[x]
Definitions unfolded in proof :  rleq: x ≤ y uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a member: t ∈ T rnonneg: rnonneg(x) all: x:A. B[x] le: A ≤ B not: ¬A implies:  Q false: False uall: [x:A]. B[x] subtype_rel: A ⊆B prop: real: iff: ⇐⇒ Q rev_implies:  Q
Lemmas referenced :  less_than'_wf rsub_wf nat_plus_wf rnonneg_wf uiff_wf real_wf rleq_wf req_wf rnonneg_functionality rsub_functionality req_weakening
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity independent_pairFormation isect_memberFormation introduction cut hypothesis sqequalRule sqequalHypSubstitution lambdaEquality dependent_functionElimination thin hypothesisEquality productElimination independent_pairEquality voidElimination lemma_by_obid isectElimination applyEquality because_Cache minusEquality natural_numberEquality axiomEquality equalityTransitivity equalitySymmetry cumulativity setElimination rename isect_memberEquality addLevel independent_isectElimination independent_functionElimination

\mforall{}[x1,x2,y1,y2:\mBbbR{}].    (uiff(x1  \mleq{}  y1;x2  \mleq{}  y2))  supposing  ((y1  =  y2)  and  (x1  =  x2))

Date html generated: 2016_05_18-AM-07_05_16
Last ObjectModification: 2015_12_28-AM-00_36_27

Theory : reals

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