Expression of type Conditional

from the theory of proveit.logic.sets.intersection

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, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import InSet, Intersect
from proveit.logic.sets import x_in_every_A

# build up the expression from sub-expressions
expr = Conditional(x_in_every_A, InSet(x, Intersect(A_1_to_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(x \in A_{1}\right) \land  \left(x \in A_{2}\right) \land  \ldots \land  \left(x \in A_{m}\right) \textrm{ if } x \in \left(A_{1} \cap  A_{2} \cap  \ldots \cap  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: 13 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	18, 7
6	ExprRange	lambda_map: 8 start_index: 16 end_index: 17
7	Operation	operator: 9 operands: 10
8	Lambda	parameter: 22 body: 11
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operands: 14
12	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
13	Literal
14	ExprTuple	18, 19
15	Lambda	parameter: 22 body: 19
16	Literal
17	Variable
18	Variable
19	IndexedVar	variable: 20 index: 22
20	Variable
21	ExprTuple	22
22	Variable