Expression of type Conditional

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

# build up the expression from sub-expressions
expr = Conditional(InSet(Lambda(x, Mod(Add(x, c), N)), Bijections(Interval(a, b), Interval(zero, subtract(N, one)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer)))

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 \mapsto \left(\left(x + c\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] \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 17 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Lambda	parameter: 33 body: 12
7	Operation	operator: 13 operands: 14
8	Operation	operator: 17 operands: 15
9	Operation	operator: 17 operands: 16
10	Operation	operator: 17 operands: 18
11	ExprTuple	33
12	Operation	operator: 19 operands: 20
13	Literal
14	ExprTuple	21, 22
15	ExprTuple	29, 23
16	ExprTuple	30, 23
17	Literal
18	ExprTuple	34, 23
19	Literal
20	ExprTuple	24, 37
21	Operation	operator: 26 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Operation	operator: 35 operands: 28
25	ExprTuple	29, 30
26	Literal
27	ExprTuple	31, 32
28	ExprTuple	33, 34
29	Variable
30	Variable
31	Literal
32	Operation	operator: 35 operands: 36
33	Variable
34	Variable
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal