Nuprl Lemma : int_iseg_properties
∀[i,j:ℤ]. ∀[y:{i...j}]. ((i ≤ y) ∧ (y ≤ j))
Proof
Definitions occuring in Statement :
int_iseg: {i...j},
uall: ∀[x:A]. B[x],
le: A ≤ B,
and: P ∧ Q,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_iseg: {i...j},
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
squash: ↓T
Lemmas referenced :
int_iseg_wf,
squash_wf,
less_than'_wf,
sq_stable__le,
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,
productElimination,
independent_pairEquality,
voidElimination,
axiomEquality,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}[i,j:\mBbbZ{}]. \mforall{}[y:\{i...j\}]. ((i \mleq{} y) \mwedge{} (y \mleq{} j))
Date html generated:
2016_05_13-PM-04_02_08
Last ObjectModification:
2016_01_14-PM-07_24_35
Theory : int_1
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