Nuprl Lemma : rat-complex-boundary_wf
∀[k,n:ℕ]. ∀[K:n-dim-complex]. (∂(K) ∈ n - 1-dim-complex)
Proof
Definitions occuring in Statement :
rat-complex-boundary: ∂(K),
rational-cube-complex: n-dim-complex,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtract: n - m,
natural_number: $n
Definitions unfolded in proof :
nat_plus: ℕ+,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
ge: i ≥ j ,
rat-complex-boundary: ∂(K),
int_seg: {i..j-},
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
true: True,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
top: Top,
cand: A c∧ B,
and: P ∧ Q,
rational-cube-complex: n-dim-complex,
guard: {T},
implies: P ⇒ Q,
sq_type: SQType(T),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
in-complex-boundary_wf,
istype-less_than,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
face-complex_wf,
istype-le,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
subtract_wf,
rat-cube-sub-complex_wf,
l_member_wf,
istype-int,
lelt_wf,
set_subtype_base,
rat-cube-dimension_wf,
equal-wf-base,
l_all_wf2,
compatible-rat-cubes_wf,
pairwise_wf2,
no_repeats_wf,
l_all_nil,
pairwise-nil,
istype-void,
no_repeats_nil,
rational-cube_wf,
nil_wf,
boundary-of-0-dim-is-nil,
istype-nat,
rational-cube-complex_wf,
int_subtype_base,
subtype_base_sq,
decidable__equal_int
Rules used in proof :
int_eqEquality,
dependent_pairFormation_alt,
approximateComputation,
setIsType,
baseClosed,
addEquality,
minusEquality,
applyEquality,
lambdaEquality_alt,
productIsType,
independent_pairFormation,
voidElimination,
dependent_set_memberEquality_alt,
productElimination,
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
universeIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
independent_functionElimination,
because_Cache,
independent_isectElimination,
intEquality,
cumulativity,
isectElimination,
instantiate,
unionElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k,n:\mBbbN{}]. \mforall{}[K:n-dim-complex]. (\mpartial{}(K) \mmember{} n - 1-dim-complex)
Date html generated:
2019_10_29-AM-07_58_32
Last ObjectModification:
2019_10_19-PM-10_31_27
Theory : rationals
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