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, d
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import Equals, Set

# build up the expression from sub-expressions
expr = Conditional(Equals(Set(a_1_to_m, b, c_1_to_n), Set(a_1_to_m, d, c_1_to_n)).with_wrapping_at(2), Equals(b, d))

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\{\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{m}, d,c_{1}, c_{2}, \ldots, c_{n}\right\} \end{array} \end{array} \textrm{ if } b = d\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	11, 13
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	12, 11, 14
9	Literal
10	ExprTuple	12, 13, 14
11	Variable
12	ExprRange	lambda_map: 15 start_index: 18 end_index: 16
13	Variable
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