Nuprl Lemma : not-gt
∀x,y:ℤ. uiff(¬(y > x);x ≥ y )
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 :
ge: i ≥ j ,
gt: i > j,
le: A ≤ B,
less_than: a < b,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
member_wf,
and_wf,
squash_wf,
not_wf,
less_than'_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
thin,
sqequalHypSubstitution,
hypothesis,
independent_functionElimination,
hypothesisEquality,
imageMemberEquality,
baseClosed,
lemma_by_obid,
isectElimination,
voidElimination,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
intEquality,
imageElimination
Latex:
\mforall{}x,y:\mBbbZ{}. uiff(\mneg{}(y > x);x \mgeq{} y )
Date html generated:
2016_05_13-PM-03_29_47
Last ObjectModification:
2016_01_14-PM-06_41_44
Theory : arithmetic
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