Nuprl Lemma : no_repeats_from-upto
∀[n1,n2:ℤ]. no_repeats(ℤ;[n1, n2))
Proof
Definitions occuring in Statement :
from-upto: [n, m),
no_repeats: no_repeats(T;l),
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
no_repeats: no_repeats(T;l),
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff
Lemmas referenced :
length-from-upto,
equal_wf,
select_wf,
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,
le_wf,
less_than_wf,
not_wf,
nat_wf,
length_wf,
from-upto_wf,
no_repeats_witness,
subtype_rel_list,
lt_int_wf,
lelt_wf,
subtract_wf,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__equal_int,
equal-wf-base,
int_subtype_base,
assert_wf,
bnot_wf,
intformless_wf,
int_formula_prop_less_lemma,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
select-from-upto
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
because_Cache,
independent_functionElimination,
voidElimination,
independent_isectElimination,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll,
applyEquality,
setEquality,
productEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
productElimination,
instantiate,
cumulativity,
impliesFunctionality
Latex:
\mforall{}[n1,n2:\mBbbZ{}]. no\_repeats(\mBbbZ{};[n1, n2))
Date html generated:
2017_04_17-AM-07_55_50
Last ObjectModification:
2017_02_27-PM-04_28_32
Theory : list_1
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