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, L, x
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(Mod(x, L), x), InSet(x, Interval(zero, subtract(L, 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(x ~\textup{mod}~ L\right) = x \textrm{ if } x \in \{0~\ldotp \ldotp~L - 1\}\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 13
5	Literal
6	ExprTuple	13, 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 18
11	Literal
12	ExprTuple	14, 15
13	Variable
14	Literal
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	18, 19
18	Variable
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	Literal