Nuprl Lemma : rat-complex-subdiv-polyhedron
∀[k,n:ℕ]. ∀[K:n-dim-complex]. |(K)'| ≡ |K|
Proof
Definitions occuring in Statement :
rat-cube-complex-polyhedron: |K|,
nat: ℕ,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
rat-complex-subdiv: (K)',
rational-cube-complex: n-dim-complex
Definitions unfolded in proof :
cand: A c∧ B,
rev_implies: P ⇐ Q,
false: False,
not: ¬A,
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
rational-cube-complex: n-dim-complex,
rat-cube-complex-polyhedron: |K|,
subtype_rel: A ⊆r B,
and: P ∧ Q,
ext-eq: A ≡ B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
is-half-cube_wf,
istype-assert,
in-some-half-cube,
in-rat-half-cube,
member-rat-complex-subdiv2,
istype-nat,
rational-cube-complex_wf,
rat-cube-complex-polyhedron_wf,
istype-void,
l_exists_iff,
not_wf,
l_member_wf,
in-rat-cube_wf,
rat-complex-subdiv_wf,
rational-cube_wf,
l_exists_wf,
double-negation-hyp-elim
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
voidElimination,
productIsType,
dependent_pairFormation_alt,
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
axiomEquality,
independent_pairEquality,
functionIsType,
productElimination,
dependent_functionElimination,
lambdaFormation_alt,
independent_functionElimination,
universeIsType,
setIsType,
sqequalRule,
because_Cache,
applyEquality,
hypothesis,
isectElimination,
extract_by_obid,
hypothesisEquality,
dependent_set_memberEquality_alt,
rename,
thin,
setElimination,
sqequalHypSubstitution,
lambdaEquality_alt,
independent_pairFormation,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k,n:\mBbbN{}]. \mforall{}[K:n-dim-complex]. |(K)'| \mequiv{} |K|
Date html generated:
2019_11_04-PM-04_43_43
Last ObjectModification:
2019_10_31-AM-11_05_26
Theory : real!vectors
Home
Index