Nuprl Lemma : add_mono_wrt_le

`∀[a,b,n:ℤ].  uiff(a ≤ b;(a + n) ≤ (b + n))`

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` le: `A ≤ B` add: `n + m` 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` le: `A ≤ B` not: `¬A` implies: `P `` Q` false: `False` prop: `ℙ` all: `∀x:A. B[x]` top: `Top` subtract: `n - m` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` decidable: `Dec(P)` or: `P ∨ Q`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation sqequalHypSubstitution productElimination thin hypothesis sqequalRule independent_pairEquality lambdaEquality dependent_functionElimination hypothesisEquality because_Cache lemma_by_obid isectElimination addEquality axiomEquality equalityTransitivity equalitySymmetry voidElimination isect_memberEquality intEquality independent_isectElimination natural_numberEquality multiplyEquality voidEquality dependent_set_memberEquality imageMemberEquality baseClosed independent_functionElimination unionElimination

Latex:
\mforall{}[a,b,n:\mBbbZ{}].    uiff(a  \mleq{}  b;(a  +  n)  \mleq{}  (b  +  n))

Date html generated: 2016_05_13-PM-03_40_04
Last ObjectModification: 2016_01_14-PM-06_38_47

Theory : arithmetic

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