Nuprl Lemma : no_repeats_filter
∀[T:Type]. ∀[P:T ⟶ 𝔹]. ∀[l:T List]. no_repeats(T;filter(P;l)) supposing no_repeats(T;l)
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
filter: filter(P;l),
list: T List,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
not: ¬A,
false: False
Lemmas referenced :
iff_weakening_uiff,
no_repeats_wf,
filter_wf5,
subtype_rel_dep_function,
bool_wf,
l_member_wf,
subtype_rel_self,
set_wf,
uall_wf,
isect_wf,
l_before_wf,
not_wf,
equal_wf,
no_repeats_iff,
no_repeats_witness,
list_wf,
l_before_filter
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
applyEquality,
sqequalRule,
lambdaEquality,
hypothesis,
setEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
lambdaFormation,
independent_functionElimination,
productElimination,
voidElimination,
dependent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[l:T List]. no\_repeats(T;filter(P;l)) supposing no\_repeats(T;l)
Date html generated:
2017_04_17-AM-07_26_56
Last ObjectModification:
2017_02_27-PM-04_05_55
Theory : list_1
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