Nuprl Lemma : compat-no_repeats_common-member
∀[T:Type]. ∀[L1,L2:T List].
(∀[i:ℕ||L1||]. ∀[j:ℕ||L2||]. i = j ∈ ℤ supposing L1[i] = L2[j] ∈ T) supposing
((no_repeats(T;L1) ∧ no_repeats(T;L2)) and
L1 || L2)
Proof
Definitions occuring in Statement :
compat: l1 || l2,
no_repeats: no_repeats(T;l),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
compat: l1 || l2,
or: P ∨ Q,
iseg: l1 ≤ l2,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
no_repeats: no_repeats(T;l),
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
squash: ↓T,
top: Top,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
less_than: a < b,
nat: ℕ
Lemmas referenced :
decidable__equal_int,
int_seg_subtype_nat,
length_wf,
false_wf,
length_wf_nat,
equal_wf,
nat_wf,
less_than_wf,
squash_wf,
true_wf,
length_append,
subtype_rel_list,
top_wf,
iff_weakening_equal,
non_neg_length,
int_seg_properties,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermAdd_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
nat_properties,
intformeq_wf,
int_formula_prop_eq_lemma,
list_wf,
select_append_front,
select_wf,
decidable__le,
length-append,
int_seg_wf,
no_repeats_wf,
compat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
extract_by_obid,
dependent_functionElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isectElimination,
applyEquality,
natural_numberEquality,
cumulativity,
independent_isectElimination,
sqequalRule,
independent_pairFormation,
lambdaFormation,
dependent_set_memberEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
addEquality,
dependent_pairFormation,
int_eqEquality,
computeAll,
hyp_replacement,
applyLambdaEquality,
axiomEquality,
productEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List].
(\mforall{}[i:\mBbbN{}||L1||]. \mforall{}[j:\mBbbN{}||L2||]. i = j supposing L1[i] = L2[j]) supposing
((no\_repeats(T;L1) \mwedge{} no\_repeats(T;L2)) and
L1 || L2)
Date html generated:
2018_05_21-PM-06_44_53
Last ObjectModification:
2017_07_26-PM-04_55_21
Theory : general
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