Expression of type ExprTuple

from the theory of proveit.logic.sets.enumeration

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, ExprTuple, Lambda, n, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Equals, Forall, InSet, NotInSet, Set
from proveit.logic.sets import x_notequals_all_y
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = Equals(NotInSet(x, Set(y_1_to_n)), x_notequals_all_y)), InSet(n, Natural))))

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(n \mapsto \left\{\forall_{x, y_{1}, y_{2}, \ldots, y_{n}}~\left(\left(x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) = \left(\left(x \neq y_{1}\right) \land  \left(x \neq y_{2}\right) \land  \ldots \land  \left(x \neq y_{n}\right)\right)\right) \textrm{ if } n \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	31, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	34, 27
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	34, 22
20	Literal
21	ExprTuple	23
22	Operation	operator: 24 operands: 25
23	ExprRange	lambda_map: 26 start_index: 30 end_index: 31
24	Literal
25	ExprTuple	27
26	Lambda	parameter: 38 body: 28
27	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
28	Operation	operator: 32 operands: 33
29	Lambda	parameter: 38 body: 35
30	Literal
31	Variable
32	Literal
33	ExprTuple	34, 35
34	Variable
35	IndexedVar	variable: 36 index: 38
36	Variable
37	ExprTuple	38
38	Variable