Nuprl Lemma : cycle_wf
∀[n:ℕ]. ∀[L:ℕn List]. (cycle(L) ∈ ℕn ⟶ ℕn)
Proof
Definitions occuring in Statement :
cycle: cycle(L),
list: T List,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cycle: cycle(L),
nat: ℕ,
all: ∀x:A. B[x],
or: P ∨ Q,
let: let,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
bfalse: ff,
int_seg: {i..j-},
prop: ℙ,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
guard: {T},
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
nil: [],
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b)
Lemmas referenced :
int_seg_wf,
list-cases,
null_nil_lemma,
list_ind_nil_lemma,
product_subtype_list,
null_cons_lemma,
list_ind_cons_lemma,
reduce_hd_cons_lemma,
list_wf,
nat_wf,
eq_int_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
equal_wf,
bnot_wf,
not_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
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,
less_than_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
spread_cons_lemma,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
hd_wf,
cons_wf,
length_cons_ge_one,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
unionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
lambdaEquality,
baseClosed,
intEquality,
lambdaFormation,
equalityElimination,
independent_functionElimination,
independent_isectElimination,
independent_pairFormation,
impliesFunctionality,
intWeakElimination,
dependent_pairFormation,
int_eqEquality,
computeAll,
applyEquality,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
instantiate,
cumulativity,
imageElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[L:\mBbbN{}n List]. (cycle(L) \mmember{} \mBbbN{}n {}\mrightarrow{} \mBbbN{}n)
Date html generated:
2017_04_17-AM-08_16_59
Last ObjectModification:
2017_02_27-PM-04_40_37
Theory : list_1
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