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
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