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, c, x
from proveit.logic import Equals, SetOfAll
from proveit.numbers import Add, Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = Equals(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(c, 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(c + x\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}} = \{0~\ldotp \ldotp~N - 1\}

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: 5 operand: 8
4	Operation	operator: 29 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 32 body: 12
9	Literal
10	Operation	operator: 27 operands: 13
11	ExprTuple	32
12	Conditional	value: 14 condition: 15
13	ExprTuple	24, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operand: 26
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	32, 25
21	Literal
22	ExprTuple	26
23	Operation	operator: 27 operands: 28
24	Variable
25	Operation	operator: 29 operands: 30
26	Literal
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Variable
33	Variable
34	Variable