Expression of type Equals

from the theory of proveit.logic.sets.disjointness

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.core_expr_types import x_1_to_n
from proveit.logic import Disjoint, Distinct, Equals
from proveit.logic.sets import x_singletons_range

# build up the expression from sub-expressions
expr = Equals(Distinct(x_1_to_n), Disjoint(x_singletons_range))

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())

\textrm{distinct}\left(x_{1}, x_{2}, \ldots, x_{n}\right) = \textrm{disjoint}\left(\left\{x_{1}\right\}, \left\{x_{2}\right\}, \ldots, \left\{x_{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	9
7	Literal
8	ExprTuple	10
9	ExprRange	lambda_map: 11 start_index: 13 end_index: 14
10	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
11	Lambda	parameter: 21 body: 18
12	Lambda	parameter: 21 body: 15
13	Literal
14	Variable
15	Operation	operator: 16 operand: 18
16	Literal
17	ExprTuple	18
18	IndexedVar	variable: 19 index: 21
19	Variable
20	ExprTuple	21
21	Variable