Nuprl Lemma : rat-complex-subdiv_wf
∀[k,n:ℕ]. ∀[K:n-dim-complex]. ((K)' ∈ n-dim-complex)
Proof
Definitions occuring in Statement :
rat-complex-subdiv: (K)',
rational-cube-complex: n-dim-complex,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
sq_stable: SqStable(P),
true: True,
pi2: snd(t),
pi1: fst(t),
rat-point-interval: [a],
rat-interval-face: I ≤ J,
rat-cube-face: c ≤ d,
band: p ∧b q,
rat-interval-intersection: I ⋂ J,
is-half-interval: is-half-interval(I;J),
inhabited-rat-interval: Inhabited(I),
rational-interval: ℚInterval,
rat-cube-intersection: c ⋂ d,
rev_uimplies: rev_uimplies(P;Q),
l_all: (∀x∈L.P[x]),
compatible-rat-cubes: Compatible(c;d),
rational-cube: ℚCube(k),
rev_implies: P ⇐ Q,
l_disjoint: l_disjoint(T;l1;l2),
less_than': less_than'(a;b),
no_repeats: no_repeats(T;l),
decidable: Dec(P),
squash: ↓T,
less_than: a < b,
le: A ≤ B,
lelt: i ≤ j < k,
pairwise: (∀x,y∈L. P[x; y]),
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
rat-complex-subdiv: (K)',
cand: A c∧ B,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
ge: i ≥ j ,
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
rat-cube-dimension: dim(c),
iff: P ⇐⇒ Q,
prop: ℙ,
uimplies: b supposing a,
so_apply: x[s],
nat: ℕ,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
rational-cube-complex: n-dim-complex,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
half-cube-dimension,
compatible-half-cubes,
member-rat-complex-subdiv,
compatible-rat-cubes-refl,
compatible-rat-cubes-symm,
Error :pairwise-iff,
sq_stable__no_repeats,
member_map,
qavg-eq-iff-7,
istype-true,
qle_reflexivity,
qavg-eq-iff-8,
qle-qavg-iff-4,
qavg-eq-iff-2,
member_wf,
uiff_transitivity,
qavg-same,
istype-universe,
true_wf,
squash_wf,
uiff_transitivity3,
qavg-eq-iff-4,
qavg-eq-iff-3,
qavg-eq-iff-1,
qavg-qle-iff-2,
qle_antisymmetry,
qmin-eq-iff-2,
qmax-eq-iff-2,
qmin-eq-iff-1,
qmax-eq-iff-1,
qmax-eq-iff,
qmin-eq-iff,
rat-interval-intersection_wf,
rat-interval-face_wf,
qle_transitivity_qorder,
qle-qavg-iff-1,
qavg-qle-iff-1,
subtype_rel_self,
rational-interval_wf,
qmin_ub,
qmax_lb,
assert_of_band,
assert_of_bor,
iff_transitivity,
iff_weakening_equal,
assert-q_le-eq,
q_le_wf,
rationals_wf,
equal_wf,
bfalse_wf,
assert-qeq,
btrue_wf,
band_wf,
qeq_wf2,
bor_wf,
qmin_wf,
qmax_wf,
qavg_wf,
qle_wf,
rat-cube-intersection_wf,
assert-inhabited-rat-cube,
assert-is-half-cube,
is-half-interval_wf,
iff_weakening_uiff,
is-half-cube_wf,
select_wf,
istype-false,
int_seg_subtype_nat,
select-map,
istype-less_than,
int_formula_prop_less_lemma,
intformless_wf,
istype-le,
int_formula_prop_not_lemma,
intformnot_wf,
decidable__le,
decidable__lt,
int_seg_properties,
top_wf,
subtype_rel_list,
length_wf,
int_seg_wf,
length-map,
no_repeats-concat,
istype-nat,
rational-cube-complex_wf,
l_all_wf2,
compatible-rat-cubes_wf,
pairwise_wf2,
no_repeats_wf,
istype-assert,
half-cubes-of_wf,
list_wf,
map_wf,
concat_wf,
assert_wf,
subtype_rel_list_set,
assert_witness,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
istype-void,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
itermConstant_wf,
intformeq_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
assert_of_bnot,
eqff_to_assert,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
inhabited-rat-cube_wf,
l_member_wf,
le_wf,
int_subtype_base,
istype-int,
lelt_wf,
set_subtype_base,
rat-cube-dimension_wf,
equal-wf-base,
l_all_iff,
rational-cube_wf,
list-subtype
Rules used in proof :
baseClosed,
imageMemberEquality,
universeEquality,
functionIsType,
functionExtensionality,
independent_pairEquality,
hyp_replacement,
inrFormation_alt,
inlFormation_alt,
unionEquality,
productEquality,
unionIsType,
promote_hyp,
functionEquality,
sqequalBase,
applyLambdaEquality,
imageElimination,
isectIsTypeImplies,
axiomEquality,
productIsType,
dependent_set_memberEquality_alt,
equalityIstype,
setEquality,
independent_pairFormation,
voidElimination,
isect_memberEquality_alt,
int_eqEquality,
dependent_pairFormation_alt,
approximateComputation,
equalitySymmetry,
equalityTransitivity,
cumulativity,
instantiate,
unionElimination,
independent_functionElimination,
universeIsType,
inhabitedIsType,
setIsType,
because_Cache,
independent_isectElimination,
addEquality,
natural_numberEquality,
minusEquality,
intEquality,
lambdaEquality_alt,
sqequalRule,
dependent_functionElimination,
productElimination,
lambdaFormation_alt,
applyEquality,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k,n:\mBbbN{}]. \mforall{}[K:n-dim-complex]. ((K)' \mmember{} n-dim-complex)
Date html generated:
2019_10_29-AM-07_59_33
Last ObjectModification:
2019_10_22-AM-00_44_15
Theory : rationals
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