Expression of type Conditional

from the theory of proveit.logic.booleans.conjunction

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.core_expr_types import A_1_to_m
from proveit.logic import And, Boolean, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(And(A_1_to_m), Boolean), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, m)))

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} \land  A_{2} \land  \ldots \land  A_{m}\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} \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: 7 operands: 4
3	ExprTuple	5, 18
4	ExprTuple	6
5	Operation	operator: 7 operands: 8
6	ExprRange	lambda_map: 9 start_index: 13 end_index: 14
7	Literal
8	ExprTuple	10
9	Lambda	parameter: 21 body: 11
10	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
11	Operation	operator: 15 operands: 16
12	Lambda	parameter: 21 body: 17
13	Literal
14	Variable
15	Literal
16	ExprTuple	17, 18
17	IndexedVar	variable: 19 index: 21
18	Literal
19	Variable
20	ExprTuple	21
21	Variable