Nuprl Lemma : rat-cube-diameter_wf
∀[k:ℕ]. ∀[c:ℚCube(k)]. (rat-cube-diameter(k;c) ∈ ℝ)
Proof
Definitions occuring in Statement :
rat-cube-diameter: rat-cube-diameter(k;c),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rational-cube: ℚCube(k)
Definitions unfolded in proof :
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
rational-interval: ℚInterval,
prop: ℙ,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
ge: i ≥ j ,
squash: ↓T,
less_than: a < b,
rational-cube: ℚCube(k),
le: A ≤ B,
and: P ∧ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
nat: ℕ,
rat-cube-diameter: rat-cube-diameter(k;c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
int_seg_wf,
istype-less_than,
istype-le,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermSubtract_wf,
itermAdd_wf,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
int_seg_properties,
rat2real_wf,
rsub_wf,
int-to-real_wf,
rmax_wf,
subtract_wf,
rsum_wf
Rules used in proof :
isectIsTypeImplies,
axiomEquality,
addEquality,
because_Cache,
equalitySymmetry,
equalityTransitivity,
equalityIstype,
lambdaFormation_alt,
inhabitedIsType,
productIsType,
universeIsType,
voidElimination,
isect_memberEquality_alt,
int_eqEquality,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
independent_pairFormation,
imageElimination,
dependent_set_memberEquality_alt,
applyEquality,
productElimination,
lambdaEquality_alt,
hypothesis,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
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)]. (rat-cube-diameter(k;c) \mmember{} \mBbbR{})
Date html generated:
2019_10_31-AM-06_03_16
Last ObjectModification:
2019_10_30-PM-11_45_14
Theory : real!vectors
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