Nuprl Lemma : l_contains-no_repeats-length
∀[T:Type]. ∀[as,bs:T List]. (||as|| ≤ ||bs||) supposing (as ⊆ bs and no_repeats(T;as))
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
no_repeats: no_repeats(T;l),
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l_contains: A ⊆ B,
l_member: (x ∈ l),
l_all: (∀x∈L.P[x]),
exists: ∃x:A. B[x],
int_seg: {i..j-},
subtype_rel: A ⊆r B,
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
guard: {T},
all: ∀x:A. B[x],
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
le: A ≤ B,
so_lambda: λ2x.t[x],
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
so_apply: x[s],
pi1: fst(t),
inject: Inj(A;B;f),
no_repeats: no_repeats(T;l),
less_than': less_than'(a;b),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
injection_le,
length_wf_nat,
int_seg_wf,
length_wf,
non_neg_length,
int_seg_properties,
decidable__le,
lelt_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
inject_wf,
less_than'_wf,
l_contains_wf,
no_repeats_wf,
list_wf,
exists_wf,
nat_wf,
less_than_wf,
equal_wf,
select_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
all_wf,
decidable__equal_int_seg,
int_seg_subtype_nat,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
squash_wf,
true_wf,
iff_weakening_equal,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
promote_hyp,
thin,
productElimination,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
independent_isectElimination,
dependent_pairFormation,
functionExtensionality,
dependent_set_memberEquality,
applyEquality,
natural_numberEquality,
because_Cache,
independent_pairFormation,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_pairEquality,
axiomEquality,
universeEquality,
productEquality,
imageElimination,
lambdaFormation,
independent_functionElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. (||as|| \mleq{} ||bs||) supposing (as \msubseteq{} bs and no\_repeats(T;as))
Date html generated:
2017_04_17-AM-07_29_44
Last ObjectModification:
2017_02_27-PM-04_07_44
Theory : list_1
Home
Index