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core
/
init
.
control
.
functor
source
Imports
init.core
init.function
init.meta.name
Imported by
init.control.applicative
functor
functor
.
map_const_rev
source
@[class]
structure
functor
(f :
Type
u
→
Type
v
)
:
Type
(max (u+1) v)
map :
Π
{α β :
Type
?}
,
(α
→
β)
→
f α
→
f β
map_const :
Π
{α β :
Type
?}
,
α
→
f β
→
f α
Instances of this typeclass
bifunctor.functor
applicative.to_functor
traversable.to_functor
tagged_format.is_functor
widget.attr.is_functor
widget.html.is_functor
functor.const.functor
functor.add_const.functor
functor.comp.functor
tactic.interactive.ac_mono_ctx'.functor
filter.functor
ultrafilter.functor
Instances of other typeclasses for
functor
functor.has_sizeof_inst
source
@[reducible]
def
functor
.
map_const_rev
{f :
Type
u
→
Type
v
}
[
functor
f]
{α β :
Type
u}
:
f β
→
α
→
f α
Equations
functor.map_const_rev
=
λ (a :
f β)
(b : α),
b
<$
a
General documentation
index
foundational types
tactics
commands
hole commands
attributes
notes
references
Additional documentation
Library
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option
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data
array
basic
slice
bool
basic
lemmas
char
basic
classes
lemmas
fin
basic
ops
int
basic
bitwise
comp_lemmas
order
list
basic
instances
lemmas
qsort
nat
basic
bitwise
div
gcd
lemmas
option
basic
instances
ordering
basic
lemmas
sigma
basic
lex
string
basic
ops
subtype
basic
instances
sum
basic
unsigned
basic
ops
prod
punit
quot
repr
set
setoid
to_string
meta
converter
conv
interactive
lean
parser
smt
congruence_closure
ematch
interactive
rsimp
smt_tactic
widget
basic
html_cmd
interactive_expr
replace_save_info
tactic_component
ac_tactics
async_tactic
attribute
backward
case_tag
comp_value_tactics
congr_lemma
congr_tactic
constructor_tactic
contradiction_tactic
declaration
derive
environment
exceptional
expr
expr_address
feature_search
float
format
fun_info
has_reflect
hole_command
injection_tactic
instance_cache
interaction_monad
interactive
interactive_base
json
level
local_context
match_tactic
mk_dec_eq_instance
mk_has_reflect_instance
mk_has_sizeof_instance
mk_inhabited_instance
module_info
name
occurrences
options
pexpr
rb_map
rec_util
ref
relation_tactics
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set_get_option_tactics
simp_tactic
tactic
tagged_format
task
type_context
vm
well_founded_tactics
cc_lemmas
classical
coe
core
default
function
funext
ite_simp
logic
propext
util
version
wf
system
io
io_interface
random
mathlib
algebra
algebra
subalgebra
basic
tower
basic
bilinear
equiv
hom
operations
pi
prod
restrict_scalars
spectrum
tower
big_operators
multiset
basic
lemmas
associated
basic
fin
finprod
finsupp
intervals
nat_antidiagonal
option
order
pi
ring
ring_equiv
char_p
basic
invertible
two
char_zero
defs
infinite
lemmas
quotient
direct_sum
basic
decomposition
finsupp
module
divisibility
basic
units
euclidean_domain
basic
defs
instances
field
basic
defs
opposite
free_monoid
basic
gcd_monoid
basic
finset
multiset
group
with_one
defs
basic
commutator
commute
conj
defs
inj_surj
opposite
order_synonym
pi
prod
semiconj
type_tags
ulift
units
group_power
basic
lemmas
order
ring
group_ring_action
basic
subobjects
group_with_zero
units
basic
lemmas
basic
commute
defs
divisibility
inj_surj
power
semiconj
hom
equiv
units
basic
group_with_zero
basic
aut
commute
embedding
group
group_action
group_instances
iterate
non_unital_alg
ring
units
module
submodule
basic
bilinear
lattice
pointwise
algebra
basic
big_operators
equiv
hom
linear_map
opposites
pi
prod
ulift
monoid_algebra
basic
division
support
order
field
canonical
basic
defs
basic
defs
inj_surj
power
group
abs
bounds
defs
inj_surj
instances
min_max
order_iso
type_tags
units
hom
basic
monoid
cancel
basic
defs
canonical
defs
with_zero
basic
defs
basic
defs
lemmas
min_max
nat_cast
order_dual
prod
type_tags
units
with_top
nonneg
field
floor
ring
positive
ring
ring
abs
canonical
char_zero
defs
inj_surj
lemmas
with_top
sub
canonical
defs
with_top
absolute_value
archimedean
floor
invertible
kleene
module
pi
smul
to_interval_mod
with_zero
zero_le_one
polynomial
big_operators
regular
basic
smul
ring
add_aut
aut
basic
commute
comp_typeclasses
defs
divisibility
equiv
fin
idempotents
inj_surj
opposite
pi
prod
regular
semiconj
ulift
units
star
basic
big_operators
module
order
pi
pointwise
prod
self_adjoint
star_alg_hom
subalgebra
unitary
abs
add_torsor
associated
bounds
covariant_and_contravariant
geom_sum
indicator_function
invertible
modeq
ne_zero
opposites
parity
periodic
punit_instances
quotient
smul_with_zero
support
analysis
asymptotics
asymptotic_equivalent
asymptotics
theta
calculus
deriv
add
basic
comp
inverse
mul
polynomial
pow
slope
fderiv
add
basic
bilinear
comp
equiv
linear
mul
prod
restrict_scalars
cont_diff
cont_diff_def
formal_multilinear_series
inverse
lagrange_multipliers
local_extr
mean_value
tangent_cone
complex
basic
convex
cone
basic
specific_functions
basic
basic
combination
function
hull
jensen
normed
segment
slope
star
strict
strict_convex_space
topology
uniform
inner_product_space
adjoint
basic
calculus
dual
orthogonal
pi_L2
positive
projection
rayleigh
spectrum
symmetric
locally_convex
balanced_core_hull
basic
bounded
polar
normed
field
basic
group
add_circle
add_torsor
basic
completion
hom
infinite_sum
pointwise
quotient
seminorm
order
basic
mul_action
normed_space
hahn_banach
extension
star
basic
add_torsor
affine_isometry
banach
basic
bounded_linear_maps
completion
continuous_linear_map
dual
extend
finite_dimension
is_R_or_C
linear_isometry
multilinear
operator_norm
pi_Lp
pointwise
ray
riesz_lemma
units
special_functions
complex
arg
log
log
basic
pow
complex
nnreal
real
trigonometric
angle
basic
inverse
exp
sqrt
specific_limits
basic
normed
von_neumann_algebra
basic
mean_inequalities
seminorm
combinatorics
composition
partition
control
monad
basic
traversable
basic
derive
instances
lemmas
applicative
basic
bifunctor
equiv_functor
functor
data
bool
basic
set
complex
basic
exponential
module
countable
basic
defs
dfinsupp
basic
dlist
basic
enat
basic
lattice
fin
tuple
basic
basic
interval
vec_notation
finite
basic
card
defs
set
finset
basic
card
fin
fold
image
lattice
locally_finite
n_ary
nat_antidiagonal
noncomm_prod
option
order
pairwise
pi
pointwise
powerset
preimage
prod
sigma
sort
sum
finsupp
antidiagonal
basic
defs
fin
indicator
multiset
order
to_dfinsupp
fintype
basic
big_operators
card
fin
lattice
list
option
order
perm
pi
powerset
prod
sigma
sort
sum
units
vector
fun_like
basic
embedding
equiv
int
cast
basic
defs
field
lemmas
prod
dvd
basic
order
basic
lemmas
units
basic
bitwise
char_zero
div
gcd
interval
least_greatest
lemmas
modeq
parity
succ_pred
units
is_R_or_C
basic
lemmas
list
big_operators
basic
lemmas
basic
chain
count
cycle
dedup
defs
duplicate
fin_range
forall2
infix
join
lattice
lex
min_max
nat_antidiagonal
nodup
nodup_equiv_fin
of_fn
pairwise
perm
permutation
prime
range
rotate
sort
sublists
tfae
zip
matrix
basic
basis
block
dmatrix
invertible
kronecker
notation
pequiv
multiset
antidiagonal
basic
bind
dedup
finset_ops
fold
lattice
nat_antidiagonal
nodup
pi
powerset
range
sort
sum
mv_polynomial
basic
comm_ring
equiv
rename
variables
nat
cast
basic
defs
field
prod
choose
basic
cast
sum
factorial
basic
cast
factorization
basic
gcd
basic
order
basic
lemmas
basic
bits
bitwise
count
factors
interval
lattice
log
modeq
multiplicity
pairing
parity
part_enat
periodic
pow
prime
prime_fin
set
size
sqrt
succ_pred
totient
units
with_bot
num
basic
option
basic
defs
n_ary
pi
algebra
lex
pnat
basic
defs
interval
polynomial
degree
definitions
lemmas
trailing_degree
algebra_map
basic
cancel_leads
coeff
derivative
div
erase_lead
eval
expand
field_division
induction
inductions
integral_normalization
lifts
monic
monomial
reverse
ring_division
splits
prod
basic
lex
pprod
rat
basic
big_operators
cast
defs
floor
init
lemmas
meta_defs
order
rbmap
basic
rbtree
default_lt
init
real
basic
cau_seq
cau_seq_completion
conjugate_exponents
ennreal
nnreal
pointwise
sqrt
set
intervals
basic
disjoint
group
infinite
instances
monoid
ord_connected
order_iso
pi
proj_Icc
unordered_interval
pairwise
basic
lattice
pointwise
basic
big_operators
finite
interval
list_of_fn
smul
Union_lift
accumulate
basic
bool_indicator
countable
finite
function
functor
image
lattice
list
n_ary
prod
semiring
sigma
set_like
basic
setoid
basic
sigma
basic
lex
string
defs
sum
basic
order
sym
basic
vector
basic
zmod
basic
defs
bracket
mllist
part
pequiv
quot
sign
subtype
tree
ulift
dynamics
fixed_points
basic
periodic_pts
field_theory
minpoly
basic
field
finiteness
subfield
tower
group_theory
group_action
sub_mul_action
pointwise
basic
big_operators
conj_act
defs
group
opposite
pi
prod
quotient
sub_mul_action
units
perm
cycle
basic
type
basic
fin
list
option
sign
subgroup
support
subgroup
actions
basic
finite
mul_opposite
pointwise
zpowers
submonoid
basic
center
centralizer
membership
operations
pointwise
subsemigroup
basic
center
centralizer
operations
archimedean
commutator
congruence
coset
divisible
finiteness
index
monoid_localization
order_of_element
quotient_group
linear_algebra
affine_space
affine_equiv
affine_map
affine_subspace
basic
basis
combination
independent
midpoint
midpoint_zero
restrict
slope
basis
bilinear
charpoly
basic
direct_sum
finsupp
tensor_product
eigenspace
basic
minpoly
free_module
finite
basic
matrix
rank
basic
rank
strong_rank_condition
matrix
charpoly
basic
coeff
linear_map
adjugate
basis
bilinear_form
block
determinant
general_linear_group
hermitian
mv_polynomial
nondegenerate
nonsingular_inverse
polynomial
pos_def
reindex
sesquilinear_form
special_linear_group
spectrum
symmetric
to_lin
to_linear_equiv
trace
multilinear
basic
basis
tensor_product
projective_space
basic
quadratic_form
basic
alternating
basic
basis
bilinear_form
bilinear_map
contraction
determinant
dfinsupp
dimension
dual
finite_dimensional
finrank
finsupp
finsupp_vector_space
general_linear_group
invariant_basis_number
isomorphisms
linear_independent
linear_pmap
pi
prod
projection
quotient
ray
sesquilinear_form
span
std_basis
tensor_product
tensor_product_basis
trace
unitary_group
logic
embedding
basic
set
encodable
basic
lattice
equiv
basic
defs
fin
fintype
functor
list
local_equiv
nat
option
set
transfer_instance
function
basic
conjugate
iterate
small
basic
basic
denumerable
is_empty
nonempty
nontrivial
pairwise
relation
relator
unique
meta
expr
expr_lens
rb_map
univs
number_theory
padics
padic_val
divisors
order
bounds
basic
order_iso
conditionally_complete_lattice
basic
finset
group
filter
archimedean
at_top_bot
bases
basic
cofinite
countable_Inter
extr
interval
lift
n_ary
pi
pointwise
prod
small_sets
ultrafilter
heyting
basic
hom
basic
bounded
complete_lattice
lattice
order
set
monotone
basic
rel_iso
basic
set
succ_pred
basic
limit
relation
upper_lower
basic
antichain
antisymmetrization
atoms
basic
boolean_algebra
bounded
bounded_order
chain
circular
closure
compactly_generated
compare
complete_boolean_algebra
complete_lattice
complete_lattice_intervals
copy
cover
directed
disjoint
fixed_points
galois_connection
initial_seg
iterate
jordan_holder
lattice
lattice_intervals
liminf_limsup
locally_finite
max
min_max
minimal
modular_lattice
omega_complete_partial_order
order_iso_nat
partial_sups
prop_instances
rel_classes
sup_indep
symm_diff
synonym
well_founded
well_founded_set
with_bot
zorn
zorn_atoms
ring_theory
adjoin
basic
fg
tower
coprime
basic
lemmas
ideal
basic
local_ring
operations
quotient
quotient_operations
int
basic
localization
basic
fraction_ring
integer
mv_polynomial
symmetric
polynomial
basic
content
pochhammer
quotient
scale_roots
tower
vieta
subring
basic
subsemiring
basic
valuation
basic
algebra_tower
algebraic
congruence
euclidean_domain
finite_type
finiteness
integral_closure
jacobson_ideal
matrix_algebra
multiplicity
nilpotent
noetherian
non_zero_divisors
polynomial_algebra
principal_ideal_domain
simple_module
tensor_product
unique_factorization_domain
set_theory
cardinal
basic
cofinality
finite
ordinal
schroeder_bernstein
ordinal
arithmetic
basic
exponential
fixed_point
principal
tactic
converter
apply_congr
interactive
old_conv
linarith
datatypes
elimination
frontend
lemmas
parsing
preprocessing
verification
lint
basic
default
frontend
misc
simp
type_classes
monotonicity
basic
interactive
nth_rewrite
basic
congr
default
abel
algebra
alias
apply
apply_fun
assert_exists
auto_cases
binder_matching
by_contra
cache
cancel_denoms
chain
choose
clear
compute_degree
congr
congrm
core
dec_trivial
delta_instance
dependencies
derive_fintype
derive_inhabited
doc_commands
elide
explode
ext
field_simp
fin_cases
find
finish
generalize_proofs
generalizes
group
hint
interactive
interactive_expr
interval_cases
itauto
lean_core_docs
lift
linear_combination
localized
mk_iff_of_inductive_prop
mk_simp_attribute
noncomm_ring
nontriviality
norm_cast
norm_num
obviously
pi_instances
positivity
pretty_cases
print_sorry
project_dir
protected
push_neg
rcases
rename_var
replacer
reserved_notation
restate_axiom
rewrite
ring
ring_exp
scc
show_term
simp_command
simp_result
simp_rw
simpa
simps
solve_by_elim
split_ifs
squeeze
suggest
tauto
tfae
tidy
to_additive
transform_decl
trunc_cases
unify_equations
where
with_local_reducibility
wlog
zify
topology
algebra
group
basic
infinite_sum
basic
module
order
real
ring
module
basic
determinant
finite_dimension
multilinear
simple
star
strong_topology
weak_dual
order
archimedean
compact
extend_from
field
group
intermediate_value
left_right
liminf_limsup
monotone_continuity
monotone_convergence
proj_Icc
ring
basic
ideal
affine
algebra
const_mul_action
constructions
field
filter_basis
group_completion
group_with_zero
monoid
mul_action
polynomial
star
star_subalgebra
uniform_convergence
uniform_group
uniform_mul_action
uniform_ring
bornology
basic
constructions
hom
continuous_function
basic
instances
add_circle
ennreal
int
matrix
nat
nnreal
rat
real
real_vector_space
sign
metric_space
algebra
antilipschitz
baire
basic
completion
emetric_space
hausdorff_distance
isometric_smul
isometry
lipschitz
order
basic
sets
closeds
compacts
opens
uniform_space
abstract_completion
basic
cauchy
compact
complete_separated
completion
equicontinuity
equiv
pi
separation
uniform_convergence
uniform_convergence_topology
uniform_embedding
G_delta
bases
basic
compact_open
connected
constructions
continuous_on
dense_embedding
extend_from
homeomorph
inseparable
local_extr
local_homeomorph
locally_finite
maps
nhds_set
noetherian_space
order
path_connected
quasi_separated
separation
sequences
subset_properties
support
tactic
unit_interval
monlib
linear_algebra
my_ips
basic
frob
functional
ips
mat_ips
minimal_proj
mul_op
nontracial
op_unop
pos
quantum_set
rank_one
strict
symm
tensor_hilbert
vn
my_matrix
basic
conj
include_block
is_almost_hermitian
pos_def_rpow
pos_eq_linear_map_is_positive
reshape
spectra
star_ordered_ring
End
blackbox
direct_sum_from_to
inner_aut
invariant_submodule
is_proj'
is_real
kronecker_to_tensor
lmul_rmul
mul''
my_bimodule
my_spec
my_tensor_product
nacgor
of_norm
pi_direct_sum
pi_star_ordered_ring
tensor_finite
to_matrix_of_equiv
other
sonia
preq
complex
dite
equiv
finset
is_R_or_C_le
ites
star_alg_equiv
quantum_graph
example
iso
mess
nontracial
qam_A
qam_A_example
schur_idempotent
symm
to_projections
rep_theory
aut_mat
Color scheme
dark
system
light