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 A, Conditional, ExprRange, IndexedVar, Variable, m
from proveit.logic import And, Boolean, InSet, Or
from proveit.numbers import Add, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
sub_expr3 = Add(m, one)
expr = Conditional(InSet(Or(ExprRange(sub_expr1, sub_expr2, one, sub_expr3)), Boolean), And(ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, sub_expr3)))

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} \lor  A_{2} \lor  \ldots \lor  A_{m + 1}\right) \in \mathbb{B} \textrm{ if } \left(A_{1} \in \mathbb{B}\right) \land  \left(A_{2} \in \mathbb{B}\right) \land  \ldots \land  \left(A_{m + 1} \in \mathbb{B}\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: 15 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 20
4	Literal
5	ExprTuple	7
6	Operation	operator: 8 operands: 9
7	ExprRange	lambda_map: 10 start_index: 22 end_index: 14
8	Literal
9	ExprTuple	11
10	Lambda	parameter: 25 body: 12
11	ExprRange	lambda_map: 13 start_index: 22 end_index: 14
12	Operation	operator: 15 operands: 16
13	Lambda	parameter: 25 body: 19
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	IndexedVar	variable: 23 index: 25
20	Literal
21	Variable
22	Literal
23	Variable
24	ExprTuple	25
25	Variable