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, m, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall, InSet, Intersect, NotInSet
from proveit.logic.sets import x_notin_some_A
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = Equals(NotInSet(x, Intersect(A_1_to_m)), x_notin_some_A)), InSet(m, NaturalPos))

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\{\forall_{x, A_{1}, A_{2}, \ldots, A_{m}}~\left(\left(x \notin \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\right)\right) = \left(\left(x \notin A_{1}\right) \lor  \left(x \notin A_{2}\right) \lor  \ldots \lor  \left(x \notin A_{m}\right)\right)\right) \textrm{ if } m \in \mathbb{N}^+\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 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	27, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	30, 23
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 28 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	30, 18
16	Literal
17	ExprTuple	19
18	Operation	operator: 20 operands: 21
19	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
20	Literal
21	ExprTuple	23
22	Lambda	parameter: 34 body: 24
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Operation	operator: 28 operands: 29
25	Lambda	parameter: 34 body: 31
26	Literal
27	Variable
28	Literal
29	ExprTuple	30, 31
30	Variable
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable