Expression of type Conditional

from the theory of proveit.logic.booleans.disjunction

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 B, Conditional
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import Boolean, InSet, Or

# build up the expression from sub-expressions
expr = Conditional(InSet(B, Boolean), InSet(Or(A_1_to_m, B, C_1_to_n), Boolean))

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\{B \in \mathbb{B} \textrm{ if } \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) \in \mathbb{B}\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	11, 7
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operands: 9
7	Literal
8	Literal
9	ExprTuple	10, 11, 12
10	ExprRange	lambda_map: 13 start_index: 16 end_index: 14
11	Variable
12	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
13	Lambda	parameter: 23 body: 18
14	Variable
15	Lambda	parameter: 23 body: 19
16	Literal
17	Variable
18	IndexedVar	variable: 20 index: 23
19	IndexedVar	variable: 21 index: 23
20	Variable
21	Variable
22	ExprTuple	23
23	Variable