Nuprl Lemma : not-le
∀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],
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
cand: A c∧ B
Lemmas referenced :
less_than'_wf,
less_than_wf,
le_wf,
not_wf,
decidable__lt
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
unionElimination,
independent_pairFormation,
isect_memberFormation,
isectElimination,
introduction,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
intEquality,
imageElimination,
productElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}x,y:\mBbbZ{}. uiff(\mneg{}(x \mleq{} y);y < x)
Date html generated:
2016_05_13-PM-03_29_44
Last ObjectModification:
2016_01_14-PM-06_41_57
Theory : arithmetic
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