Nuprl Lemma : cardinality-le-no_repeats-length
∀[T:Type]. ∀[k:ℕ]. ∀[L:T List]. (||L|| ≤ k) supposing (no_repeats(T;L) and |T| ≤ k)
Proof
Definitions occuring in Statement :
cardinality-le: |T| ≤ n,
no_repeats: no_repeats(T;l),
length: ||as||,
list: T List,
nat: ℕ,
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,
cardinality-le: |T| ≤ n,
exists: ∃x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
nat: ℕ,
prop: ℙ,
surject: Surj(A;B;f),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
pi1: fst(t),
int_seg: {i..j-},
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b,
squash: ↓T,
inject: Inj(A;B;f),
no_repeats: no_repeats(T;l),
subtype_rel: A ⊆r B,
less_than': less_than'(a;b)
Lemmas referenced :
less_than'_wf,
length_wf,
no_repeats_wf,
cardinality-le_wf,
list_wf,
nat_wf,
exists_wf,
int_seg_wf,
equal_wf,
all_wf,
pigeon-hole,
length_wf_nat,
select_wf,
int_seg_properties,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
set_wf,
lelt_wf,
decidable__equal_int_seg,
int_seg_subtype_nat,
false_wf,
le_wf,
intformeq_wf,
int_formula_prop_eq_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesis,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
universeEquality,
promote_hyp,
natural_numberEquality,
applyEquality,
functionExtensionality,
dependent_pairFormation,
lambdaFormation,
independent_functionElimination,
independent_isectElimination,
unionElimination,
int_eqEquality,
intEquality,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
hyp_replacement,
Error :applyLambdaEquality,
dependent_set_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[k:\mBbbN{}]. \mforall{}[L:T List]. (||L|| \mleq{} k) supposing (no\_repeats(T;L) and |T| \mleq{} k)
Date html generated:
2016_10_21-AM-10_12_40
Last ObjectModification:
2016_07_12-AM-05_30_28
Theory : list_1
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