Expression of type InSet

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 Lambda, N, a, b, c, x
from proveit.logic import Bijections, InSet
from proveit.numbers import Add, Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = InSet(Lambda(x, Mod(Add(c, x), N)), Bijections(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[x \mapsto \left(\left(c + x\right) ~\textup{mod}~ N\right)\right] \in \left[\{a~\ldotp \ldotp~b\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~N - 1\}\right]

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