Nuprl Lemma : map-permute_list
∀[g:Top]. ∀[L:Top List]. ∀[f:ℕ||L|| ⟶ ℕ||L||]. (map(g;(L o f)) ~ (map(g;L) o f))
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],
top: Top,
function: x:A ⟶ B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
permute_list: (L o f),
mklist: mklist(n;f),
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
label: ...$L... t,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
sq_type: SQType(T),
all: ∀x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
int_seg: {i..j-},
lelt: i ≤ j < k,
nequal: a ≠ b ∈ T
Lemmas referenced :
int_seg_wf,
length_wf,
top_wf,
list_wf,
subtype_base_sq,
int_subtype_base,
equal_wf,
squash_wf,
true_wf,
length-map-sq,
iff_weakening_equal,
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,
le_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
nat_wf,
primrec0_lemma,
map_nil_lemma,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
primrec-unroll,
map_append_sq,
map_cons_lemma,
select-map,
decidable__lt,
lelt_wf,
length_wf_nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
because_Cache,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
dependent_functionElimination,
lambdaFormation,
setElimination,
rename,
intWeakElimination,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
unionElimination,
equalityElimination,
promote_hyp,
functionExtensionality,
dependent_set_memberEquality
Latex:
\mforall{}[g:Top]. \mforall{}[L:Top List]. \mforall{}[f:\mBbbN{}||L|| {}\mrightarrow{} \mBbbN{}||L||]. (map(g;(L o f)) \msim{} (map(g;L) o f))
Date html generated:
2018_05_21-PM-06_54_05
Last ObjectModification:
2017_07_26-PM-04_59_04
Theory : general
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