### Nuprl Lemma : le_transitivity

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

Proof

Definitions occuring in Statement :  uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` rev_uimplies: `rev_uimplies(P;Q)` all: `∀x:A. B[x]` prop: `ℙ` le: `A ≤ B` not: `¬A` implies: `P `` Q` false: `False` squash: `↓T` subtract: `n - m` top: `Top` true: `True`
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

Latex:
\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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