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, 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 = ExprTuple(Lambda([i, j, k], 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(\left(i, j, k\right) \mapsto \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..\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	parameters: 2 body: 3
2	ExprTuple	33, 35, 38
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	11, 12, 13
10	Lambda	parameters: 14 body: 15
11	Operation	operator: 18 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	28, 30, 29, 31
15	Operation	operator: 20 operands: 21
16	ExprTuple	33, 22
17	ExprTuple	35, 22
18	Literal
19	ExprTuple	38, 22
20	Literal
21	ExprTuple	23, 24
22	Literal
23	Operation	operator: 26 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 30, 29, 30, 31
26	Literal
27	ExprTuple	28, 29, 30, 31
28	ExprRange	lambda_map: 32 start_index: 37 end_index: 33
29	ExprRange	lambda_map: 34 start_index: 37 end_index: 35
30	Variable
31	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
32	Lambda	parameter: 46 body: 39
33	Variable
34	Lambda	parameter: 46 body: 40
35	Variable
36	Lambda	parameter: 46 body: 41
37	Literal
38	Variable
39	IndexedVar	variable: 42 index: 46
40	IndexedVar	variable: 43 index: 46
41	IndexedVar	variable: 44 index: 46
42	Variable
43	Variable
44	Variable
45	ExprTuple	46
46	Variable