Nuprl Lemma : minus_mono_wrt_eq
∀[i,j:ℤ]. uiff(i = j ∈ ℤ;(-i) = (-j) ∈ ℤ)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
minus: -n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
equal_wf,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
add-mul-special,
zero-mul,
zero-add,
add-commutes,
add-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
minusEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
addEquality,
applyEquality,
lambdaEquality,
voidElimination,
voidEquality,
natural_numberEquality
Latex:
\mforall{}[i,j:\mBbbZ{}]. uiff(i = j;(-i) = (-j))
Date html generated:
2016_05_13-PM-03_40_25
Last ObjectModification:
2015_12_26-AM-09_40_24
Theory : arithmetic
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