Nuprl Lemma : bag-member-sq-list-member
∀[T:Type]. ∀L:T List. ∀x:T. ↓(x ∈ L) supposing x ↓∈ L
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
squash: ↓T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
empty-bag: {},
uiff: uiff(P;Q),
and: P ∧ Q,
false: False,
squash: ↓T,
cons-bag: x.b,
sq_or: a ↓∨ b,
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T}
Lemmas referenced :
equal_wf,
cons_wf,
cons_member,
bag-member-cons,
nil_wf,
bag-member-empty-iff,
list_wf,
l_member_wf,
squash_wf,
list-subtype-bag,
bag-member_wf,
isect_wf,
all_wf,
list_induction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
because_Cache,
applyEquality,
independent_isectElimination,
hypothesis,
independent_functionElimination,
productElimination,
voidElimination,
imageElimination,
imageMemberEquality,
baseClosed,
voidEquality,
rename,
unionElimination,
dependent_functionElimination,
inlFormation,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
inrFormation
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}x:T. \mdownarrow{}(x \mmember{} L) supposing x \mdownarrow{}\mmember{} L
Date html generated:
2016_05_15-PM-02_39_50
Last ObjectModification:
2016_01_16-AM-08_48_29
Theory : bags
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