Nuprl Lemma : le_transitivity

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


Definitions occuring in Statement :  uimplies: supposing a uall: [x:A]. B[x] le: A ≤ B int:
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a rev_uimplies: rev_uimplies(P;Q) all: x:A. B[x] prop: le: A ≤ B not: ¬A implies:  Q false: False squash: T subtract: m top: Top true: True
Lemmas referenced :  le-iff-nonneg add-nonneg subtract_wf less_than'_wf le_wf true_wf squash_wf zero-add zero-mul add-mul-special add-swap add-associates add-commutes minus-one-mul
Rules used in proof :  cut introduction extract_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin hypothesisEquality hypothesis productElimination independent_isectElimination dependent_functionElimination because_Cache intEquality isect_memberFormation sqequalRule independent_pairEquality lambdaEquality axiomEquality isect_memberEquality equalityTransitivity equalitySymmetry voidElimination baseClosed imageMemberEquality imageElimination applyEquality hyp_replacement natural_numberEquality minusEquality multiplyEquality addEquality voidEquality

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

Date html generated: 2019_06_20-AM-11_22_59
Last ObjectModification: 2018_08_01-PM-04_17_48

Theory : arithmetic

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