Nuprl Lemma : bag-member-from-upto
∀[n,m,x:ℤ]. uiff(x ↓∈ [n, m);(n ≤ x) ∧ x < m)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
from-upto: [n, m),
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
le: A ≤ B,
and: P ∧ Q,
int: ℤ
Definitions unfolded in proof :
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,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bag-member: x ↓∈ bs,
squash: ↓T
Lemmas referenced :
from-upto-member,
iff_weakening_uiff,
bag-member-list,
iff_transitivity,
uiff_wf,
decidable__int_equal,
subtype_rel_list,
l_member_wf,
list-subtype-bag,
from-upto_wf,
bag-member_wf,
less_than_wf,
le_wf,
and_wf,
member-less_than,
less_than'_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
sqequalRule,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
axiomEquality,
independent_isectElimination,
because_Cache,
intEquality,
applyEquality,
setEquality,
setElimination,
rename,
lambdaFormation,
cumulativity,
addLevel,
independent_functionElimination,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n,m,x:\mBbbZ{}]. uiff(x \mdownarrow{}\mmember{} [n, m);(n \mleq{} x) \mwedge{} x < m)
Date html generated:
2016_05_15-PM-02_39_08
Last ObjectModification:
2016_01_16-AM-08_48_49
Theory : bags
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