Nuprl Lemma : rat-complex-boundary-iter-subdiv
∀k,n,j:ℕ. ∀K:n-dim-complex. permutation(ℚCube(k);∂(K'^(j));∂(K)'^(j))
Proof
Definitions occuring in Statement :
rat-complex-iter-subdiv: K'^(n),
rat-complex-boundary: ∂(K),
rational-cube-complex: n-dim-complex,
rational-cube: ℚCube(k),
permutation: permutation(T;L1;L2),
nat: ℕ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
false: False,
rat-complex-iter-subdiv: K'^(n),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
rat-complex-subdiv: (K)',
concat: concat(ll),
reduce: reduce(f;k;as),
list_ind: list_ind,
map: map(f;as),
nil: [],
subtype_rel: A ⊆r B,
rational-cube-complex: n-dim-complex,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
cand: A c∧ B
Lemmas referenced :
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
istype-nat,
rat-complex-boundary-0-dim,
rat-complex-iter-subdiv_wf,
istype-void,
istype-le,
rational-cube-complex_wf,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
subtract-1-ge-0,
primrec0_lemma,
primrec-unroll,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
permutation-nil,
rational-cube_wf,
permutation_weakening,
rat-complex-boundary_wf,
permutation_wf,
subtract_wf,
decidable__le,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
primrec-wf2,
rat-complex-boundary-subdiv,
rat-complex-subdiv_wf,
permutation_transitivity,
permutation-when-no_repeats,
sq_stable__no_repeats,
member-permutation,
l_member_wf,
istype-assert,
is-half-cube_wf,
member-rat-complex-subdiv2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
unionElimination,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
inhabitedIsType,
sqequalRule,
dependent_set_memberEquality_alt,
independent_pairFormation,
voidElimination,
universeIsType,
intWeakElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
axiomSqEquality,
functionIsTypeImplies,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
equalityIstype,
promote_hyp,
applyEquality,
functionIsType,
setIsType,
functionEquality,
imageMemberEquality,
baseClosed,
imageElimination,
productIsType
Latex:
\mforall{}k,n,j:\mBbbN{}. \mforall{}K:n-dim-complex. permutation(\mBbbQ{}Cube(k);\mpartial{}(K'\^{}(j));\mpartial{}(K)'\^{}(j))
Date html generated:
2020_05_20-AM-09_24_25
Last ObjectModification:
2019_11_02-PM-10_35_18
Theory : rationals
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