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, N, a, b, x
from proveit.logic import SetOfAll
from proveit.numbers import Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = ExprTuple(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = Interval(a, b)), Interval(zero, subtract(N, one)))

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\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}, \{0~\ldotp \ldotp~N - 1\}\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: 3 operand: 6
2	Operation	operator: 26 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 23 body: 10
7	Literal
8	Operation	operator: 11 operands: 12
9	ExprTuple	23
10	Conditional	value: 13 condition: 14
11	Literal
12	ExprTuple	22, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operand: 25
16	Literal
17	ExprTuple	23, 22
18	Literal
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	25
22	Variable
23	Variable
24	Operation	operator: 26 operands: 27
25	Literal
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Variable