Expression of type Equals

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 N, a, b, x
from proveit.logic import Card, Equals, SetOfAll
from proveit.numbers import Interval, Mod

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = sub_expr1)), Card(sub_expr1))

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\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = |\{a~\ldotp \ldotp~b\}|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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