Expression of type Equals

from the theory of proveit.logic.sets.enumeration

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 x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Equals, NotInSet, Set
from proveit.logic.sets import x_notequals_all_y

# build up the expression from sub-expressions
expr = Equals(NotInSet(x, Set(y_1_to_n)), x_notequals_all_y)

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(x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) = \left(\left(x \neq y_{1}\right) \land  \left(x \neq y_{2}\right) \land  \ldots \land  \left(x \neq y_{n}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	21, 9
7	Literal
8	ExprTuple	10
9	Operation	operator: 11 operands: 12
10	ExprRange	lambda_map: 13 start_index: 17 end_index: 18
11	Literal
12	ExprTuple	14
13	Lambda	parameter: 25 body: 15
14	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
15	Operation	operator: 19 operands: 20
16	Lambda	parameter: 25 body: 22
17	Literal
18	Variable
19	Literal
20	ExprTuple	21, 22
21	Variable
22	IndexedVar	variable: 23 index: 25
23	Variable
24	ExprTuple	25
25	Variable