Nuprl Lemma : singleton-complex_wf
∀[k,n:ℕ]. ∀[c:{c:ℚCube(k)| dim(c) = n ∈ ℤ} ].  (singleton-complex(c) ∈ n-dim-complex)
Proof
Definitions occuring in Statement : 
singleton-complex: singleton-complex(c)
, 
rational-cube-complex: n-dim-complex
, 
rat-cube-dimension: dim(c)
, 
rational-cube: ℚCube(k)
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
singleton-complex: singleton-complex(c)
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
all: ∀x:A. B[x]
, 
so_lambda: λ2x y.t[x; y]
, 
top: Top
, 
so_apply: x[s1;s2]
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
, 
true: True
, 
so_lambda: λ2x.t[x]
, 
subtype_rel: A ⊆r B
, 
int_seg: {i..j-}
, 
nat: ℕ
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
rational-cube-complex: n-dim-complex
, 
prop: ℙ
Lemmas referenced : 
no_repeats_singleton, 
rational-cube_wf, 
pairwise-singleton, 
istype-void, 
l_all_cons, 
equal-wf-base, 
rat-cube-dimension_wf, 
set_subtype_base, 
lelt_wf, 
int_subtype_base, 
le_wf, 
nil_wf, 
l_all_nil, 
cons_wf, 
no_repeats_wf, 
pairwise_wf2, 
compatible-rat-cubes_wf, 
l_all_wf2, 
l_member_wf, 
istype-int, 
istype-nat
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
setElimination, 
thin, 
rename, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
independent_pairFormation, 
dependent_functionElimination, 
isect_memberEquality_alt, 
voidElimination, 
productElimination, 
independent_functionElimination, 
natural_numberEquality, 
because_Cache, 
lambdaEquality_alt, 
intEquality, 
applyEquality, 
minusEquality, 
addEquality, 
inhabitedIsType, 
equalityTransitivity, 
equalitySymmetry, 
independent_isectElimination, 
dependent_set_memberEquality_alt, 
productIsType, 
universeIsType, 
instantiate, 
cumulativity, 
setIsType, 
axiomEquality, 
equalityIstype, 
sqequalBase, 
isectIsTypeImplies
Latex:
\mforall{}[k,n:\mBbbN{}].  \mforall{}[c:\{c:\mBbbQ{}Cube(k)|  dim(c)  =  n\}  ].    (singleton-complex(c)  \mmember{}  n-dim-complex)
Date html generated:
2020_05_20-AM-09_22_22
Last ObjectModification:
2019_11_13-PM-06_45_14
Theory : rationals
Home
Index