Nuprl Lemma : map_permute_list
∀[A,B:Type]. ∀[f:B ⟶ A]. ∀[x:B List]. ∀[g:ℕ||x|| ⟶ ℕ||x||]. (map(f;(x o g)) = (map(f;x) o g) ∈ (A List))
Proof
Definitions occuring in Statement :
permute_list: (L o f),
length: ||as||,
map: map(f;as),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
nat: ℕ,
true: True,
ge: i ≥ j
Lemmas referenced :
equal_wf,
map_length,
permute_list_wf,
int_seg_wf,
length_wf,
iff_weakening_equal,
permute_list_length,
map_wf,
list_extensionality,
subtype_rel_dep_function,
int_seg_subtype,
false_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
int_seg_properties,
less_than_wf,
nat_wf,
list_wf,
map_length_nat,
lelt_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
select_wf,
non_neg_length,
nat_properties,
length_wf_nat,
itermConstant_wf,
int_term_value_constant_lemma,
map_select,
permute_list_select
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
because_Cache,
hypothesis,
cumulativity,
hypothesisEquality,
functionExtensionality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
lambdaFormation,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll,
setElimination,
rename,
functionEquality,
axiomEquality,
universeEquality,
dependent_set_memberEquality,
applyLambdaEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:B {}\mrightarrow{} A]. \mforall{}[x:B List]. \mforall{}[g:\mBbbN{}||x|| {}\mrightarrow{} \mBbbN{}||x||]. (map(f;(x o g)) = (map(f;x) o g))
Date html generated:
2017_10_01-AM-08_38_29
Last ObjectModification:
2017_07_26-PM-04_27_01
Theory : list!
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