Nuprl Lemma : no_repeats_append
∀[T:Type]. ∀[l1,l2:T List]. l_disjoint(T;l1;l2) supposing no_repeats(T;l1 @ l2)
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
no_repeats: no_repeats(T;l),
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
l_disjoint: l_disjoint(T;l1;l2),
no_repeats: no_repeats(T;l),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
l_member: (x ∈ l),
and: P ∧ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
prop: ℙ,
so_lambda: λ2x.t[x],
nat: ℕ,
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
so_apply: x[s],
less_than: a < b,
squash: ↓T,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
l_member_wf,
uall_wf,
nat_wf,
isect_wf,
less_than_wf,
length_wf,
append_wf,
not_wf,
equal_wf,
select_wf,
length-append,
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,
list_wf,
itermAdd_wf,
intformless_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
le_wf,
decidable__lt,
intformeq_wf,
int_formula_prop_eq_lemma,
squash_wf,
true_wf,
select_append_front,
lelt_wf,
iff_weakening_equal,
select_append_back,
add-subtract-cancel
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
productElimination,
because_Cache,
hypothesis,
independent_functionElimination,
voidElimination,
productEquality,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
setElimination,
rename,
independent_isectElimination,
isect_memberEquality,
voidEquality,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_set_memberEquality,
addEquality,
imageElimination,
applyLambdaEquality,
applyEquality,
imageMemberEquality,
baseClosed,
hyp_replacement
Latex:
\mforall{}[T:Type]. \mforall{}[l1,l2:T List]. l\_disjoint(T;l1;l2) supposing no\_repeats(T;l1 @ l2)
Date html generated:
2017_04_17-AM-07_28_47
Last ObjectModification:
2017_02_27-PM-04_07_02
Theory : list_1
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