Nuprl Lemma : rat-complex-iter-subdiv-pos-length
∀[k,n:ℕ]. ∀[K:{K:n-dim-complex| 0 < ||K||} ]. ∀[j:ℕ]. 0 < ||K'^(j)||
Proof
Definitions occuring in Statement :
length: ||as||,
nat: ℕ,
less_than: a < b,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
natural_number: $n,
rational-cube-complex: n-dim-complex
Definitions unfolded in proof :
guard: {T},
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
or: P ∨ Q,
decidable: Dec(P),
rational-cube-complex: n-dim-complex,
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
le: A ≤ B,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
rat-complex-iter-subdiv: Error :rat-complex-iter-subdiv,
prop: ℙ,
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
assert_of_lt_int,
eqtt_to_assert,
uiff_transitivity,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
Error :rat-complex-subdiv-non-nil,
bnot_wf,
le_wf,
le_int_wf,
less_than_wf,
assert_wf,
int_subtype_base,
bool_wf,
equal-wf-base,
lt_int_wf,
istype-nat,
rational-cube-complex_wf,
int_formula_prop_not_lemma,
intformnot_wf,
decidable__le,
primrec-unroll,
subtract-1-ge-0,
istype-le,
Error :rat-complex-iter-subdiv_wf,
rational-cube_wf,
length_wf,
rless-int,
primrec0_lemma,
member-less_than,
istype-less_than,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
full-omega-unsat,
nat_properties
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
equalityIstype,
equalityElimination,
baseClosed,
closedConclusion,
baseApply,
setIsType,
unionElimination,
applyEquality,
dependent_set_memberEquality_alt,
productElimination,
because_Cache,
inhabitedIsType,
functionIsTypeImplies,
universeIsType,
independent_pairFormation,
sqequalRule,
voidElimination,
isect_memberEquality_alt,
dependent_functionElimination,
int_eqEquality,
lambdaEquality_alt,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
natural_numberEquality,
lambdaFormation_alt,
intWeakElimination,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k,n:\mBbbN{}]. \mforall{}[K:\{K:n-dim-complex| 0 < ||K||\} ]. \mforall{}[j:\mBbbN{}]. 0 < ||K'\^{}(j)||
Date html generated:
2019_11_04-PM-04_43_56
Last ObjectModification:
2019_10_31-PM-00_18_35
Theory : real!vectors
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