Nuprl Lemma : minus_functionality_wrt_lt
∀[i,j:ℤ]. -i < -j supposing i > j
Proof
Definitions occuring in Statement :
less_than: a < b
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
gt: i > j
,
minus: -n
,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uimplies: b supposing a
,
prop: ℙ
,
gt: i > j
,
all: ∀x:A. B[x]
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
subtype_rel: A ⊆r B
,
top: Top
,
subtract: n - m
,
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,
mul-distributes,
less_than_wf,
omega-shadow,
add-zero,
mul-associates,
not-lt-2,
zero-add,
zero-mul,
mul-distributes-right,
two-mul,
add-mul-special,
add-commutes,
add-swap,
one-mul,
add-associates,
minus-one-mul-top,
le_reflexive,
subtract_wf,
add_functionality_wrt_le,
less-iff-le,
member-less_than,
gt_wf,
minus-one-mul
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
minusEquality,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality,
dependent_functionElimination,
productElimination,
addEquality,
natural_numberEquality,
multiplyEquality,
applyEquality,
lambdaEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
independent_functionElimination,
unionElimination
Latex:
\mforall{}[i,j:\mBbbZ{}]. -i < -j supposing i > j
Date html generated:
2016_05_13-PM-03_40_29
Last ObjectModification:
2016_01_14-PM-06_38_44
Theory : arithmetic
Home
Index