Expression of type Conditional

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 import Conditional, n
from proveit.core_expr_types import x_1_to_n
from proveit.logic import Disjoint, Distinct, Equals, Forall, InSet
from proveit.logic.sets import x_singletons_range
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(Distinct(x_1_to_n), Disjoint(x_singletons_range))), InSet(n, NaturalPos))

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\{\forall_{x_{1}, x_{2}, \ldots, x_{n}}~\left(\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)\right) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	23, 8
7	Lambda	parameters: 15 body: 9
8	Literal
9	Operation	operator: 10 operands: 11
10	Literal
11	ExprTuple	12, 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	19
18	ExprRange	lambda_map: 20 start_index: 22 end_index: 23
19	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
20	Lambda	parameter: 30 body: 27
21	Lambda	parameter: 30 body: 24
22	Literal
23	Variable
24	Operation	operator: 25 operand: 27
25	Literal
26	ExprTuple	27
27	IndexedVar	variable: 28 index: 30
28	Variable
29	ExprTuple	30
30	Variable