Nuprl Lemma : add_cancel_in_lt
∀[a,b,n:ℤ].  a < b supposing a + n < b + n
Proof
Definitions occuring in Statement : 
less_than: a < b
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
add: n + m
, 
int: ℤ
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
subtract: n - m
, 
top: Top
, 
nat_plus: ℕ+
, 
less_than: a < b
, 
squash: ↓T
, 
less_than': less_than'(a;b)
, 
true: True
, 
implies: P 
⇒ Q
, 
le: A ≤ B
, 
not: ¬A
, 
false: False
, 
decidable: Dec(P)
, 
or: P ∨ Q
Lemmas referenced : 
decidable__lt, 
le-add-cancel-alt, 
mul-commutes, 
mul-associates, 
mul-distributes, 
omega-shadow, 
add-zero, 
minus-add, 
less-iff-le, 
zero-add, 
zero-mul, 
mul-distributes-right, 
two-mul, 
add-mul-special, 
add-associates, 
add-commutes, 
add-swap, 
one-mul, 
minus-one-mul, 
le_reflexive, 
subtract_wf, 
add_functionality_wrt_le, 
not-lt-2, 
member-less_than, 
less_than_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
hypothesis, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
addEquality, 
hypothesisEquality, 
sqequalRule, 
isect_memberEquality, 
because_Cache, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
intEquality, 
dependent_functionElimination, 
productElimination, 
multiplyEquality, 
natural_numberEquality, 
voidElimination, 
voidEquality, 
minusEquality, 
dependent_set_memberEquality, 
independent_pairFormation, 
imageMemberEquality, 
baseClosed, 
independent_functionElimination, 
unionElimination
Latex:
\mforall{}[a,b,n:\mBbbZ{}].    a  <  b  supposing  a  +  n  <  b  +  n
Date html generated:
2016_05_13-PM-03_39_43
Last ObjectModification:
2016_01_14-PM-06_38_22
Theory : arithmetic
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