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 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 = NotInSet(x, Intersect(A_1_to_m)), condition = 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(x \notin A_{1}\right) \lor  \left(x \notin A_{2}\right) \lor  \ldots \lor  \left(x \notin A_{m}\right)}~\left(x \notin \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\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	25, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	28, 21
10	Conditional	value: 11 condition: 12
11	Operation	operator: 26 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	28, 16
14	Literal
15	ExprTuple	17
16	Operation	operator: 18 operands: 19
17	ExprRange	lambda_map: 20 start_index: 24 end_index: 25
18	Literal
19	ExprTuple	21
20	Lambda	parameter: 32 body: 22
21	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
22	Operation	operator: 26 operands: 27
23	Lambda	parameter: 32 body: 29
24	Literal
25	Variable
26	Literal
27	ExprTuple	28, 29
28	Variable
29	IndexedVar	variable: 30 index: 32
30	Variable
31	ExprTuple	32
32	Variable