### Nuprl Lemma : minus-le

`∀[n,x:ℤ].  uiff((-n) ≤ x;0 ≤ (x + n))`

Proof

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

Latex:
\mforall{}[n,x:\mBbbZ{}].    uiff((-n)  \mleq{}  x;0  \mleq{}  (x  +  n))

Date html generated: 2016_05_13-PM-03_31_35
Last ObjectModification: 2016_01_14-PM-06_41_11

Theory : arithmetic

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