Nuprl Lemma : not-ge-2
∀x,y:ℤ. uiff(¬(x ≥ y );(x + 1) ≤ y)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
ge: i ≥ j ,
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],
ge: i ≥ j ,
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
less_than'_wf,
le_wf,
iff_weakening_uiff,
not_wf,
not-le-2,
uiff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
intEquality,
cut,
independent_pairFormation,
isect_memberFormation,
introduction,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
addEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
addLevel,
independent_isectElimination,
independent_functionElimination,
cumulativity
Latex:
\mforall{}x,y:\mBbbZ{}. uiff(\mneg{}(x \mgeq{} y );(x + 1) \mleq{} y)
Date html generated:
2016_05_13-PM-03_31_03
Last ObjectModification:
2015_12_26-AM-09_46_15
Theory : arithmetic
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