Expression of type Equals

from the theory of proveit.logic.sets.subtraction

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 c
from proveit.logic import Difference, Equals, InSet, NotInSet, Or, Set
from proveit.numbers import Add, four, one, three, two

# build up the expression from sub-expressions
sub_expr1 = Add(one, one)
sub_expr2 = Set(one, sub_expr1, three, Add(two, two))
sub_expr3 = Set(sub_expr1, Add(two, one), four)
expr = Equals(NotInSet(c, Difference(sub_expr2, sub_expr3)), Or(NotInSet(c, sub_expr2), InSet(c, sub_expr3)))

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(c \notin \left(\left\{1, 1 + 1, 3, 2 + 2\right\} - \left\{1 + 1, 2 + 1, 4\right\}\right)\right) = \left(\left(c \notin \left\{1, 1 + 1, 3, 2 + 2\right\}\right) \lor \left(c \in \left\{1 + 1, 2 + 1, 4\right\}\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: 13 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	18, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	17, 19
13	Literal
14	ExprTuple	18, 17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 21 operands: 20
18	Variable
19	Operation	operator: 21 operands: 22
20	ExprTuple	33, 25, 23, 24
21	Literal
22	ExprTuple	25, 26, 27
23	Literal
24	Operation	operator: 30 operands: 28
25	Operation	operator: 30 operands: 29
26	Operation	operator: 30 operands: 31
27	Literal
28	ExprTuple	32, 32
29	ExprTuple	33, 33
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Literal