Nuprl Lemma : boundary-polyhedron-subtype
∀[k:ℕ]. ∀[n:ℕ+]. ∀[K:n-dim-complex]. (|∂(K)| ⊆r |K|)
Proof
Definitions occuring in Statement :
rat-cube-complex-polyhedron: |K|,
nat_plus: ℕ+,
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
rat-complex-boundary: ∂(K),
rational-cube-complex: n-dim-complex
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
guard: {T},
true: True,
cand: A c∧ B,
l_member: (x ∈ l),
iff: P ⇐⇒ Q,
so_apply: x[s],
squash: ↓T,
less_than: a < b,
le: A ≤ B,
lelt: i ≤ j < k,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
rational-cube-complex: n-dim-complex,
prop: ℙ,
and: P ∧ Q,
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 ,
nat_plus: ℕ+,
nat: ℕ,
stable-union: Error :stable-union,
rat-cube-complex-polyhedron: |K|,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
iff_weakening_equal,
subtype_rel_self,
real-vec_wf,
true_wf,
squash_wf,
in-rat-cube-face,
istype-less_than,
member-rat-complex-boundary,
select_member,
istype-nat,
nat_plus_wf,
rational-cube-complex_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
rat-cube-complex-polyhedron_wf,
not_wf,
decidable__lt,
int_seg_properties,
select_wf,
in-rat-cube_wf,
rational-cube_wf,
length_wf,
int_seg_wf,
exists_wf,
istype-le,
int_formula_prop_wf,
int_formula_prop_less_lemma,
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,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
nat_plus_properties,
rat-complex-boundary_wf,
double-negation-hyp-elim
Rules used in proof :
universeEquality,
instantiate,
baseClosed,
imageMemberEquality,
applyEquality,
isectIsTypeImplies,
axiomEquality,
productIsType,
functionIsType,
equalitySymmetry,
equalityTransitivity,
equalityIstype,
imageElimination,
closedConclusion,
productElimination,
lambdaFormation_alt,
inhabitedIsType,
universeIsType,
independent_pairFormation,
sqequalRule,
voidElimination,
isect_memberEquality_alt,
int_eqEquality,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
natural_numberEquality,
dependent_functionElimination,
hypothesis,
because_Cache,
isectElimination,
extract_by_obid,
hypothesisEquality,
dependent_set_memberEquality_alt,
rename,
thin,
setElimination,
sqequalHypSubstitution,
lambdaEquality_alt,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[K:n-dim-complex]. (|\mpartial{}(K)| \msubseteq{}r |K|)
Date html generated:
2019_10_30-AM-10_13_25
Last ObjectModification:
2019_10_27-AM-00_21_11
Theory : real!vectors
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