Nuprl Lemma : rat-complex-boundary-iter-subdiv-polyhedron
∀[k,n:ℕ]. ∀[K:n-dim-complex]. ∀[j:ℕ]. |∂(K'^(j))| ≡ |∂(K)|
Proof
Definitions occuring in Statement :
rat-cube-complex-polyhedron: |K|,
nat: ℕ,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
rat-complex-boundary: ∂(K),
rational-cube-complex: n-dim-complex
Definitions unfolded in proof :
cand: A c∧ B,
rational-cube-complex: n-dim-complex,
less_than': less_than'(a;b),
le: A ≤ B,
prop: ℙ,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
ge: i ≥ j ,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
ext-eq: A ≡ B,
guard: {T},
implies: P ⇒ Q,
sq_type: SQType(T),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
Error :rat-complex-boundary-iter-subdiv,
permutation_inversion,
rat-cube-complex-polyhedron_wf,
subtype_rel_transitivity,
rat-complex-boundary_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
rat-complex-iter-subdiv-polyhedron,
rat-cube-complex-polyhedron_functionality,
permutation-nil,
rational-cube_wf,
nil_wf,
Error :rat-complex-iter-subdiv_wf,
subtype_rel_self,
istype-le,
int_formula_prop_le_lemma,
intformle_wf,
decidable__le,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
le_wf,
set_subtype_base,
nat_wf,
rat-complex-boundary-0-dim,
istype-nat,
rational-cube-complex_wf,
int_subtype_base,
subtype_base_sq,
decidable__equal_int
Rules used in proof :
lambdaFormation_alt,
dependent_set_memberEquality_alt,
independent_pairFormation,
voidElimination,
int_eqEquality,
dependent_pairFormation_alt,
approximateComputation,
equalitySymmetry,
equalityTransitivity,
lambdaEquality_alt,
applyEquality,
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
inhabitedIsType,
axiomEquality,
independent_pairEquality,
productElimination,
sqequalRule,
independent_functionElimination,
because_Cache,
independent_isectElimination,
intEquality,
cumulativity,
isectElimination,
instantiate,
unionElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k,n:\mBbbN{}]. \mforall{}[K:n-dim-complex]. \mforall{}[j:\mBbbN{}]. |\mpartial{}(K'\^{}(j))| \mequiv{} |\mpartial{}(K)|
Date html generated:
2019_11_04-PM-04_43_50
Last ObjectModification:
2019_11_02-PM-10_52_41
Theory : real!vectors
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