Nuprl Lemma : not-lt-2
∀x,y:ℤ. uiff(¬x < y;y ≤ x)
Proof
Definitions occuring in Statement :
less_than: a < b,
uiff: uiff(P;Q),
le: A ≤ B,
all: ∀x:A. B[x],
not: ¬A,
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,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
less_than: a < b,
cand: A c∧ B,
squash: ↓T
Lemmas referenced :
le_wf,
less_than_irreflexivity,
less_than_transitivity1,
less_than_wf,
not_wf,
less_than'_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesis,
axiomEquality,
independent_isectElimination,
independent_functionElimination,
intEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}x,y:\mBbbZ{}. uiff(\mneg{}x < y;y \mleq{} x)
Date html generated:
2016_05_13-PM-03_31_01
Last ObjectModification:
2016_01_14-PM-06_41_07
Theory : arithmetic
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