Nuprl Lemma : int_seg_properties
∀[i,j:ℤ]. ∀[y:{i..j-}]. i ≤ y < j
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
lelt: i ≤ j < k,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-},
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
uimplies: b supposing a,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
le: A ≤ B,
not: ¬A,
false: False
Lemmas referenced :
int_seg_wf,
less_than'_wf,
squash_wf,
member-less_than,
sq_stable__less_than,
sq_stable__le,
less_than_wf,
le_wf,
sq_stable__and
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
isect_memberEquality,
independent_functionElimination,
lambdaFormation,
because_Cache,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_isectElimination,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
voidElimination
Latex:
\mforall{}[i,j:\mBbbZ{}]. \mforall{}[y:\{i..j\msupminus{}\}]. i \mleq{} y < j
Date html generated:
2016_05_13-PM-04_02_04
Last ObjectModification:
2016_01_14-PM-07_24_36
Theory : int_1
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