Expression of type ExprTuple

from the theory of proveit.core_expr_types.tuples

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
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j
from proveit.logic import And, Equals, Forall, InSet
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, b_1_to_j, c_1_to_k, d_1_to_j], instance_expr = Equals([a_1_to_i, b_1_to_j, c_1_to_k], [a_1_to_i, d_1_to_j, c_1_to_k]).with_wrapping_at(2), condition = Equals([b_1_to_j], [d_1_to_j])), 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}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}, d_{1}, d_{2}, \ldots, d_{j}~|~\left(b_{1}, b_{2}, \ldots, b_{j}\right) = \left(d_{1}, d_{2}, \ldots, d_{j}\right)}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i},d_{1}, d_{2}, \ldots, d_{j},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	35, 41, 37
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	30, 32, 31, 33
15	Conditional	value: 20 condition: 21
16	ExprTuple	35, 22
17	ExprTuple	41, 22
18	Literal
19	ExprTuple	37, 22
20	Operation	operator: 24 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	ExprTuple	30, 32, 31
27	ExprTuple	30, 33, 31
28	ExprTuple	32
29	ExprTuple	33
30	ExprRange	lambda_map: 34 start_index: 40 end_index: 35
31	ExprRange	lambda_map: 36 start_index: 40 end_index: 37
32	ExprRange	lambda_map: 38 start_index: 40 end_index: 41
33	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
34	Lambda	parameter: 51 body: 42
35	Variable
36	Lambda	parameter: 51 body: 43
37	Variable
38	Lambda	parameter: 51 body: 44
39	Lambda	parameter: 51 body: 45
40	Literal
41	Variable
42	IndexedVar	variable: 46 index: 51
43	IndexedVar	variable: 47 index: 51
44	IndexedVar	variable: 48 index: 51
45	IndexedVar	variable: 49 index: 51
46	Variable
47	Variable
48	Variable
49	Variable
50	ExprTuple	51
51	Variable