Nuprl Lemma : l_contains-eq_set-no_repeats
∀[T:Type]. ∀[as,bs:T List]. ∀[eq:EqDecider(T)].
(no_repeats(T;as)) supposing (l_eqset(T;as;bs) and no_repeats(T;bs) and (||as|| = ||bs|| ∈ ℤ))
Proof
Definitions occuring in Statement :
l_eqset: l_eqset(T;L1;L2),
no_repeats: no_repeats(T;l),
length: ||as||,
list: T List,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
set-equal: set-equal(T;x;y),
all: ∀x:A. B[x],
l_eqset: l_eqset(T;L1;L2),
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q)
Lemmas referenced :
remove-repeats-length-no-repeats,
remove-repeats-set-equal,
subtype_base_sq,
int_subtype_base,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
remove-repeats-length-no-repeats-iff,
l_eqset_wf,
no_repeats_wf,
length_wf,
deq_wf,
list_wf,
no_repeats_witness
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
because_Cache,
instantiate,
cumulativity,
intEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
applyEquality,
lambdaEquality,
imageElimination,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
isect_memberFormation,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. \mforall{}[eq:EqDecider(T)].
(no\_repeats(T;as)) supposing (l\_eqset(T;as;bs) and no\_repeats(T;bs) and (||as|| = ||bs||))
Date html generated:
2017_04_17-AM-09_12_51
Last ObjectModification:
2017_02_27-PM-05_19_34
Theory : decidable!equality
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