Expression of type Conditional

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, 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 = Conditional(Equals(Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(Add(c, x), 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())

\left\{|\left\{\left(c + x\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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