Expression of type Conditional

from the theory of proveit.logic.sets.enumeration

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, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import NotInSet, Set
from proveit.logic.sets import x_notequals_all_y

# build up the expression from sub-expressions
expr = Conditional(x_notequals_all_y, NotInSet(x, Set(y_1_to_n)))

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 \neq y_{1}\right) \land  \left(x \neq y_{2}\right) \land  \ldots \land  \left(x \neq y_{n}\right) \textrm{ if } x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\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
5	Literal
6	ExprTuple	19, 8
7	ExprRange	lambda_map: 9 start_index: 17 end_index: 18
8	Operation	operator: 10 operands: 11
9	Lambda	parameter: 23 body: 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
14	Literal
15	ExprTuple	19, 20
16	Lambda	parameter: 23 body: 20
17	Literal
18	Variable
19	Variable
20	IndexedVar	variable: 21 index: 23
21	Variable
22	ExprTuple	23
23	Variable