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, b
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import NotInSet, ProperSubset, Set

# build up the expression from sub-expressions
sub_expr1 = Set(a_1_to_m)
expr = Conditional(ProperSubset(sub_expr1, Set(a_1_to_m, b, c_1_to_n)), NotInSet(b, sub_expr1))

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\{a_{1}, a_{2}, \ldots, a_{m}\right\} \subset \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\} \textrm{ if } b \notin \left\{a_{1}, a_{2}, \ldots, a_{m}\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	8, 7
5	Literal
6	ExprTuple	12, 8
7	Operation	operator: 10 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	14, 12, 13
10	Literal
11	ExprTuple	14
12	Variable
13	ExprRange	lambda_map: 15 start_index: 18 end_index: 16
14	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
15	Lambda	parameter: 25 body: 20
16	Variable
17	Lambda	parameter: 25 body: 21
18	Literal
19	Variable
20	IndexedVar	variable: 22 index: 25
21	IndexedVar	variable: 23 index: 25
22	Variable
23	Variable
24	ExprTuple	25
25	Variable