Nuprl Lemma : not-le-2
∀x,y:ℤ. uiff(¬(x ≤ y);(y + 1) ≤ x)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
le: A ≤ B,
all: ∀x:A. B[x],
not: ¬A,
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
le: A ≤ B,
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
iff_weakening_uiff,
le_wf,
less-iff-le,
less_than'_wf,
less_than_wf,
uiff_wf,
not_wf,
not-le,
add-commutes
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
addLevel,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
isect_memberFormation,
introduction,
independent_isectElimination,
lemma_by_obid,
isectElimination,
because_Cache,
addEquality,
natural_numberEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
sqequalRule,
independent_pairEquality,
lambdaEquality,
voidElimination,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
applyEquality,
isect_memberEquality,
voidEquality
Latex:
\mforall{}x,y:\mBbbZ{}. uiff(\mneg{}(x \mleq{} y);(y + 1) \mleq{} x)
Date html generated:
2016_05_13-PM-03_30_58
Last ObjectModification:
2015_12_26-AM-09_46_21
Theory : arithmetic
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