Nuprl Lemma : no_repeats-rat-cube-faces
∀k:ℕ. ∀c:ℚCube(k). no_repeats(ℚCube(k);rat-cube-faces(k;c))
Proof
Definitions occuring in Statement :
rat-cube-faces: rat-cube-faces(k;c),
rational-cube: ℚCube(k),
no_repeats: no_repeats(T;l),
nat: ℕ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
rat-cube-faces: rat-cube-faces(k;c),
mapfilter: mapfilter(f;P;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
rational-cube: ℚCube(k),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
l_disjoint: l_disjoint(T;l1;l2),
cand: A c∧ B,
uiff: uiff(P;Q),
rational-interval: ℚInterval,
pi2: snd(t),
lower-rc-face: lower-rc-face(c;j),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
sq_type: SQType(T),
guard: {T},
bfalse: ff,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
nequal: a ≠ b ∈ T ,
rat-point-interval: [a],
rat-interval-dimension: dim(I),
pi1: fst(t),
true: True,
upper-rc-face: upper-rc-face(c;j),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
no_repeats-concat,
map_wf,
int_seg_wf,
list_wf,
rational-cube_wf,
cons_wf,
lower-rc-face_wf,
upper-rc-face_wf,
nil_wf,
filter_wf5,
upto_wf,
eq_int_wf,
rat-interval-dimension_wf,
int_seg_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
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,
istype-le,
istype-less_than,
l_member_wf,
istype-nat,
pairwise-map,
l_disjoint_wf,
pairwise-iff2,
no_repeats_filter,
no_repeats_upto,
member_filter_2,
assert_of_eq_int,
not_wf,
cons_member,
l_disjoint_nil2,
iff_transitivity,
iff_weakening_uiff,
l_disjoint_cons,
eqtt_to_assert,
intformeq_wf,
int_formula_prop_eq_lemma,
subtype_base_sq,
int_subtype_base,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
q_less_wf,
equal-wf-T-base,
assert_wf,
qless_wf,
qless_transitivity_2_qorder,
qle_weakening_eq_qorder,
qless_irreflexivity,
bnot_wf,
istype-assert,
uiff_transitivity2,
assert-q_less-eq,
assert_of_bnot,
iff_weakening_equal,
member_singleton,
l_all_iff,
no_repeats_wf,
member_map,
squash_wf,
true_wf,
istype-universe,
subtype_rel_self,
no_repeats_cons,
no_repeats_singleton,
length_wf,
length_of_cons_lemma,
length_of_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality_alt,
universeIsType,
applyEquality,
dependent_set_memberEquality_alt,
productElimination,
imageElimination,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
productIsType,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
setIsType,
instantiate,
cumulativity,
functionIsType,
equalityIstype,
productEquality,
promote_hyp,
applyLambdaEquality,
equalityElimination,
intEquality,
baseClosed,
sqequalBase,
universeEquality,
imageMemberEquality
Latex:
\mforall{}k:\mBbbN{}. \mforall{}c:\mBbbQ{}Cube(k). no\_repeats(\mBbbQ{}Cube(k);rat-cube-faces(k;c))
Date html generated:
2020_05_20-AM-09_22_08
Last ObjectModification:
2019_11_27-AM-10_48_43
Theory : rationals
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