Nuprl Lemma : not-ge
∀x,y:ℤ. uiff(¬(x ≥ y );y > x)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
gt: i > j,
ge: i ≥ j ,
all: ∀x:A. B[x],
not: ¬A,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
gt: i > j,
ge: i ≥ j ,
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
not: ¬A,
false: False
Lemmas referenced :
less_than_wf,
iff_weakening_uiff,
not_wf,
le_wf,
not-le,
uiff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
intEquality,
cut,
independent_pairFormation,
isect_memberFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
addLevel,
productElimination,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
cumulativity,
introduction,
sqequalRule,
lambdaEquality,
voidElimination
Latex:
\mforall{}x,y:\mBbbZ{}. uiff(\mneg{}(x \mgeq{} y );y > x)
Date html generated:
2016_05_13-PM-03_29_46
Last ObjectModification:
2015_12_26-AM-09_47_27
Theory : arithmetic
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