Expression of type Forall

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

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

\forall_{n \in \mathbb{N}^+}~\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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 27 body: 4
3	ExprTuple	27
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	27, 12
11	Lambda	parameters: 19 body: 13
12	Literal
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23
22	ExprRange	lambda_map: 24 start_index: 26 end_index: 27
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Lambda	parameter: 34 body: 31
25	Lambda	parameter: 34 body: 28
26	Literal
27	Variable
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable