Nuprl Lemma : le-add-shift
∀[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
Lemmas referenced : 
le_wf, 
less_than'_wf, 
le_reflexive, 
add_functionality_wrt_le, 
minus-one-mul, 
add-commutes, 
add-associates, 
add-mul-special, 
zero-mul, 
zero-add, 
add-swap, 
add-zero
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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