Nuprl Lemma : le-add-cancel4
∀[c,t,t':ℤ].  uiff((c + t) ≤ t';c ≤ 0) supposing t = t' ∈ ℤ
Proof
Definitions occuring in Statement : 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
le: A ≤ B
, 
add: n + m
, 
natural_number: $n
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
prop: ℙ
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
le: A ≤ B
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
Lemmas referenced : 
le-add-cancel3, 
less_than'_wf, 
le_wf, 
equal_wf, 
zero-add
Rules used in proof : 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isectElimination, 
thin, 
hypothesisEquality, 
natural_numberEquality, 
independent_isectElimination, 
hypothesis, 
addEquality, 
intEquality, 
because_Cache, 
isect_memberFormation, 
introduction, 
sqequalRule, 
productElimination, 
independent_pairEquality, 
isect_memberEquality, 
lambdaEquality, 
dependent_functionElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
voidElimination
Latex:
\mforall{}[c,t,t':\mBbbZ{}].    uiff((c  +  t)  \mleq{}  t';c  \mleq{}  0)  supposing  t  =  t'
Date html generated:
2016_05_13-PM-03_31_22
Last ObjectModification:
2015_12_26-AM-09_46_03
Theory : arithmetic
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