Expression of type Card

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, c, x
from proveit.logic import Card, SetOfAll
from proveit.numbers import Add, Interval, Mod

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

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 + c\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}|

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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