Nuprl Lemma : map-sq-mklist
∀[L:Top List]. ∀[f:Top]. (map(f;L) ~ mklist(||L||;λi.(f L[i])))
Proof
Definitions occuring in Statement :
mklist: mklist(n;f),
select: L[n],
length: ||as||,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
mklist: mklist(n;f),
cons: [a / b],
colength: colength(L),
guard: {T},
decidable: Dec(P),
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),
le: A ≤ B,
nat_plus: ℕ+
Lemmas referenced :
nat_properties,
full-omega-unsat,
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,
top_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
int_subtype_base,
list_wf,
list-cases,
map_nil_lemma,
length_of_nil_lemma,
stuck-spread,
base_wf,
primrec0_lemma,
product_subtype_list,
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,
equal_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
decidable__equal_int,
map_cons_lemma,
length_of_cons_lemma,
mklist-add1-cons,
length_wf_nat,
length_wf,
set_wf,
non_neg_length,
mklist_add1,
select-cons-tl,
subtract-add-cancel,
decidable__lt,
add-subtract-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
sqequalAxiom,
applyEquality,
unionElimination,
baseClosed,
promote_hyp,
hypothesis_subsumption,
productElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
instantiate,
cumulativity,
imageElimination,
because_Cache
Latex:
\mforall{}[L:Top List]. \mforall{}[f:Top]. (map(f;L) \msim{} mklist(||L||;\mlambda{}i.(f L[i])))
Date html generated:
2018_05_21-PM-00_37_41
Last ObjectModification:
2018_05_19-AM-06_44_11
Theory : list_1
Home
Index