Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 39 body: 3
2	ExprTuple	39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 31 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	39, 11
9	Operation	operator: 13 operand: 15
10	Operation	operator: 13 operand: 16
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	16
15	Operation	operator: 18 operand: 20
16	Operation	operator: 18 operand: 21
17	ExprTuple	20
18	Literal
19	ExprTuple	21
20	Lambda	parameter: 38 body: 22
21	Lambda	parameter: 38 body: 24
22	Conditional	value: 25 condition: 27
23	ExprTuple	38
24	Conditional	value: 26 condition: 27
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	38, 34
31	Literal
32	ExprTuple	38, 35
33	Operation	operator: 36 operands: 37
34	Variable
35	Variable
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable