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

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` le: `A ≤ B` add: `n + m` minus: `-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]` 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 addEquality voidElimination minusEquality intEquality isect_memberEquality independent_isectElimination multiplyEquality natural_numberEquality voidEquality

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

Date html generated: 2016_05_13-PM-03_31_26
Last ObjectModification: 2015_12_26-AM-09_46_01

Theory : arithmetic

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