Nuprl Lemma : rat-cube-dimension_wf
∀[k:ℕ]. ∀[c:ℚCube(k)]. (dim(c) ∈ {-1..k + 1-})
Proof
Definitions occuring in Statement :
rat-cube-dimension: dim(c),
rational-cube: ℚCube(k),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
add: n + m,
minus: -n,
natural_number: $n
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(P;Q),
less_than': less_than'(a;b),
guard: {T},
squash: ↓T,
less_than: a < b,
le: A ≤ B,
false: False,
prop: ℙ,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
bfalse: ff,
nat: ℕ,
lelt: i ≤ j < k,
so_apply: x[s],
subtype_rel: A ⊆r B,
rational-cube: ℚCube(k),
so_lambda: λ2x.t[x],
int_seg: {i..j-},
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
rat-cube-dimension: dim(c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
le_weakening,
less_than_functionality,
int_term_value_mul_lemma,
itermMultiply_wf,
sum_bound,
int_seg_properties,
non_neg_sum,
istype-nat,
rational-cube_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
intformless_wf,
intformand_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
istype-void,
int_formula_prop_not_lemma,
istype-int,
itermConstant_wf,
intformle_wf,
intformnot_wf,
full-omega-unsat,
decidable__le,
nat_properties,
assert_of_bnot,
eqff_to_assert,
not_wf,
bnot_wf,
assert_wf,
bool_wf,
equal-wf-T-base,
uiff_transitivity,
istype-less_than,
istype-le,
int_seg_wf,
rat-interval-dimension_wf,
sum_wf,
eqtt_to_assert,
inhabited-rat-cube_wf
Rules used in proof :
multiplyEquality,
applyLambdaEquality,
imageElimination,
isectIsTypeImplies,
axiomEquality,
equalityIstype,
int_eqEquality,
voidElimination,
isect_memberEquality_alt,
dependent_pairFormation_alt,
approximateComputation,
dependent_functionElimination,
independent_functionElimination,
baseClosed,
equalitySymmetry,
equalityTransitivity,
rename,
setElimination,
addEquality,
minusEquality,
productIsType,
independent_pairFormation,
natural_numberEquality,
universeIsType,
applyEquality,
lambdaEquality_alt,
dependent_set_memberEquality_alt,
independent_isectElimination,
productElimination,
because_Cache,
equalityElimination,
unionElimination,
lambdaFormation_alt,
inhabitedIsType,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c:\mBbbQ{}Cube(k)]. (dim(c) \mmember{} \{-1..k + 1\msupminus{}\})
Date html generated:
2019_10_29-AM-07_52_02
Last ObjectModification:
2019_10_17-PM-04_41_41
Theory : rationals
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