Expression of type Conditional

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, i, j, k, x
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, x, b_1_to_j, c_1_to_k], instance_expr = Equals(Set(a_1_to_i, x, b_1_to_j, x, c_1_to_k), Set(a_1_to_i, b_1_to_j, x, c_1_to_k)).with_wrapping_at(2)), And(InSet(i, Natural), InSet(j, Natural), InSet(k, 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\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, x, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}}~\left(\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{i}, x,b_{1}, b_{2}, \ldots, b_{j}, x,c_{1}, c_{2}, \ldots, c_{k}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j}, x,c_{1}, c_{2}, \ldots, c_{k}\right\} \end{array} \end{array}\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \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	8, 9, 10
7	Lambda	parameters: 11 body: 12
8	Operation	operator: 15 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	25, 27, 26, 28
12	Operation	operator: 17 operands: 18
13	ExprTuple	30, 19
14	ExprTuple	32, 19
15	Literal
16	ExprTuple	35, 19
17	Literal
18	ExprTuple	20, 21
19	Literal
20	Operation	operator: 23 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 27, 26, 27, 28
23	Literal
24	ExprTuple	25, 26, 27, 28
25	ExprRange	lambda_map: 29 start_index: 34 end_index: 30
26	ExprRange	lambda_map: 31 start_index: 34 end_index: 32
27	Variable
28	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
29	Lambda	parameter: 43 body: 36
30	Variable
31	Lambda	parameter: 43 body: 37
32	Variable
33	Lambda	parameter: 43 body: 38
34	Literal
35	Variable
36	IndexedVar	variable: 39 index: 43
37	IndexedVar	variable: 40 index: 43
38	IndexedVar	variable: 41 index: 43
39	Variable
40	Variable
41	Variable
42	ExprTuple	43
43	Variable