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 ExprTuple, L, S, c, x
from proveit.logic import Card, SetOfAll
from proveit.numbers import Add, Mod

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(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)))

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(x + c\right) ~\textup{mod}~ L\right\}_{x \in S}|, |\left\{x ~\textup{mod}~ L\right\}_{x \in S}|\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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