Expression of type Lambda

from the theory of proveit.numbers.modular

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, L, Lambda, S, c, x
from proveit.logic import Card, Equals, InSet, SetOfAll
from proveit.numbers import Add, Mod, Real

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda(c, Conditional(Equals(Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(Add(x, c), L), domain = S)), Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(x, L), domain = S))), InSet(c, Real)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

c \mapsto \left\{|\left\{\left(x + c\right) ~\textup{mod}~ L\right\}_{x \in S}| = |\left\{x ~\textup{mod}~ L\right\}_{x \in S}| \textrm{ if } c \in \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 38 body: 2
1	ExprTuple	38
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 30 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	38, 10
8	Operation	operator: 12 operand: 14
9	Operation	operator: 12 operand: 15
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15
14	Operation	operator: 17 operand: 19
15	Operation	operator: 17 operand: 20
16	ExprTuple	19
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 37 body: 21
20	Lambda	parameter: 37 body: 23
21	Conditional	value: 24 condition: 26
22	ExprTuple	37
23	Conditional	value: 25 condition: 26
24	Operation	operator: 28 operands: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	32, 33
28	Literal
29	ExprTuple	37, 33
30	Literal
31	ExprTuple	37, 34
32	Operation	operator: 35 operands: 36
33	Variable
34	Variable
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Variable