### Nuprl Lemma : nequal-le-implies

`∀[x,y:ℤ].  ((x + 1) ≤ y) supposing ((x ≤ y) and y ≠ x)`

Proof

Definitions occuring in Statement :  uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` nequal: `a ≠ b ∈ T ` add: `n + m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` nequal: `a ≠ b ∈ T ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` implies: `P `` Q` false: `False` prop: `ℙ` uiff: `uiff(P;Q)` subtype_rel: `A ⊆r B` top: `Top` less_than': `less_than'(a;b)` true: `True` subtract: `n - m`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution productElimination thin hypothesis lemma_by_obid dependent_functionElimination addEquality hypothesisEquality natural_numberEquality unionElimination independent_pairFormation lambdaFormation voidElimination independent_functionElimination independent_isectElimination isectElimination sqequalRule applyEquality lambdaEquality isect_memberEquality voidEquality intEquality because_Cache minusEquality independent_pairEquality axiomEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[x,y:\mBbbZ{}].    ((x  +  1)  \mleq{}  y)  supposing  ((x  \mleq{}  y)  and  y  \mneq{}  x)

Date html generated: 2016_05_13-PM-03_31_41
Last ObjectModification: 2015_12_26-AM-09_46_05

Theory : arithmetic

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