Nuprl Lemma : rat-complex-boundary-0-dim
∀[k:ℕ]. ∀[K:0-dim-complex].  (∂(K) ~ [])
Proof
Definitions occuring in Statement : 
rat-complex-boundary: ∂(K)
, 
rational-cube-complex: n-dim-complex
, 
nil: []
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
natural_number: $n
, 
sqequal: s ~ t
Definitions unfolded in proof : 
false: False
, 
not: ¬A
, 
less_than': less_than'(a;b)
, 
le: A ≤ B
, 
squash: ↓T
, 
sq_stable: SqStable(P)
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
uimplies: b supposing a
, 
so_apply: x[s]
, 
nat: ℕ
, 
int_seg: {i..j-}
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
rational-cube-complex: n-dim-complex
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
istype-nat, 
istype-le, 
istype-void, 
rational-cube-complex_wf, 
boundary-of-0-dim-is-nil, 
sq_stable__equal, 
l_member_wf, 
int_subtype_base, 
istype-int, 
lelt_wf, 
set_subtype_base, 
rat-cube-dimension_wf, 
equal-wf-base, 
rational-cube_wf, 
sq_stable__l_all
Rules used in proof : 
isectIsTypeImplies, 
isect_memberEquality_alt, 
voidElimination, 
lambdaFormation_alt, 
independent_pairFormation, 
dependent_set_memberEquality_alt, 
axiomSqEquality, 
imageElimination, 
imageMemberEquality, 
functionIsTypeImplies, 
axiomEquality, 
dependent_functionElimination, 
equalitySymmetry, 
equalityTransitivity, 
inhabitedIsType, 
productElimination, 
because_Cache, 
independent_functionElimination, 
universeIsType, 
setIsType, 
baseClosed, 
independent_isectElimination, 
addEquality, 
natural_numberEquality, 
minusEquality, 
applyEquality, 
intEquality, 
lambdaEquality_alt, 
sqequalRule, 
hypothesis, 
hypothesisEquality, 
isectElimination, 
extract_by_obid, 
rename, 
thin, 
setElimination, 
sqequalHypSubstitution, 
cut, 
introduction, 
isect_memberFormation_alt, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}].  \mforall{}[K:0-dim-complex].    (\mpartial{}(K)  \msim{}  [])
Date html generated:
2019_10_29-AM-07_58_39
Last ObjectModification:
2019_10_22-AM-10_33_48
Theory : rationals
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