Expression of type Equals

from the theory of proveit.logic.sets.membership

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
from proveit.logic import And, Equals, NotEquals, TRUE
from proveit.numbers import Add, five, one, three

# build up the expression from sub-expressions
expr = Equals(And(NotEquals(a, one), NotEquals(a, Add(one, three)), NotEquals(a, three)), And(NotEquals(five, one), TRUE, NotEquals(five, three)))

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(\left(a \neq 1\right) \land \left(a \neq \left(1 + 3\right)\right) \land \left(a \neq 3\right)\right) = \left(\left(5 \neq 1\right) \land \top \land \left(5 \neq 3\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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9, 10
6	Literal
7	ExprTuple	11, 12, 13
8	Operation	operator: 18 operands: 14
9	Operation	operator: 18 operands: 15
10	Operation	operator: 18 operands: 16
11	Operation	operator: 18 operands: 17
12	Literal
13	Operation	operator: 18 operands: 19
14	ExprTuple	21, 25
15	ExprTuple	21, 20
16	ExprTuple	21, 26
17	ExprTuple	22, 25
18	Literal
19	ExprTuple	22, 26
20	Operation	operator: 23 operands: 24
21	Variable
22	Literal
23	Literal
24	ExprTuple	25, 26
25	Literal
26	Literal