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 A, B, C, D
from proveit.logic import And, Equals, NotEquals, NotInSet, Set

# build up the expression from sub-expressions
expr = Equals(NotInSet(A, Set(B, C, D)), And(NotEquals(A, B), NotEquals(A, C), NotEquals(A, D)))

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(A \notin \left\{B, C, D\right\}\right) = \left(\left(A \neq B\right) \land \left(A \neq C\right) \land \left(A \neq D\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, 11, 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 17 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	19, 20, 22
15	ExprTuple	21, 19
16	ExprTuple	21, 20
17	Literal
18	ExprTuple	21, 22
19	Variable
20	Variable
21	Variable
22	Variable