Nuprl Lemma : select_reject_permr
∀T:Type. ∀as:T List. ∀i:ℕ||as||. ([as[i] / as\[i]] ≡(T) as)
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
select: L[n],
length: ||as||,
reject: as\[i],
cons: [a / b],
list: T List,
int_seg: {i..j-},
all: ∀x:A. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T,
so_apply: x[s],
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
le: A ≤ B
Lemmas referenced :
int_seg_wf,
length_wf,
list_wf,
list_induction,
all_wf,
permr_wf,
cons_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
reject_wf,
nil_wf,
length_of_nil_lemma,
decidable__equal_int,
length_of_cons_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
squash_wf,
true_wf,
select_cons_hd,
reject_cons_hd,
subtype_rel_self,
iff_weakening_equal,
permr_weakening,
non_neg_length,
itermAdd_wf,
int_term_value_add_lemma,
select_cons_tl,
reject_cons_tl,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
permr_functionality_wrt_permr,
hd_two_swap_permr,
lelt_wf,
permr_reflex,
cons_functionality_wrt_permr
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
hypothesis,
universeEquality,
sqequalRule,
lambdaEquality,
cumulativity,
dependent_functionElimination,
because_Cache,
setElimination,
rename,
independent_isectElimination,
productElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
imageElimination,
equalityTransitivity,
equalitySymmetry,
addEquality,
applyEquality,
imageMemberEquality,
baseClosed,
instantiate,
dependent_set_memberEquality
Latex:
\mforall{}T:Type. \mforall{}as:T List. \mforall{}i:\mBbbN{}||as||. ([as[i] / as\mbackslash{}[i]] \mequiv{}(T) as)
Date html generated:
2018_05_22-AM-07_45_08
Last ObjectModification:
2018_05_19-AM-08_31_58
Theory : list_2
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