Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, c, d, i, j, k
from proveit.core_expr_types import a_1_to_i, c_1_to_j, d_1_to_k
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b, c_1_to_j, d_1_to_k], Conditional(Equals(Mult(a_1_to_i, b, c_1_to_j, d_1_to_k), Mult(a_1_to_i, c_1_to_j, b, d_1_to_k)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), InSet(b, Complex), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Complex), one, j), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), Complex), one, k)))))

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(a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j}, d_{1}, d_{2}, \ldots, d_{k}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\cdot d_{1} \cdot  d_{2} \cdot  \ldots \cdot  d_{k}\right) =  \\ \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j} \cdot b\cdot d_{1} \cdot  d_{2} \cdot  \ldots \cdot  d_{k}\right) \end{array} \end{array} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right) ,  b \in \mathbb{C}, \left(c_{1} \in \mathbb{C}\right) ,  \left(c_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(c_{j} \in \mathbb{C}\right), \left(d_{1} \in \mathbb{C}\right) ,  \left(d_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(d_{k} \in \mathbb{C}\right)\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: 15 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14
9	Operation	operator: 16 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprRange	lambda_map: 18 start_index: 34 end_index: 30
12	Operation	operator: 38 operands: 19
13	ExprRange	lambda_map: 20 start_index: 34 end_index: 32
14	ExprRange	lambda_map: 21 start_index: 34 end_index: 35
15	ExprTuple	22, 26, 23, 24
16	Literal
17	ExprTuple	22, 23, 26, 24
18	Lambda	parameter: 48 body: 25
19	ExprTuple	26, 43
20	Lambda	parameter: 48 body: 27
21	Lambda	parameter: 48 body: 28
22	ExprRange	lambda_map: 29 start_index: 34 end_index: 30
23	ExprRange	lambda_map: 31 start_index: 34 end_index: 32
24	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
25	Operation	operator: 38 operands: 36
26	Variable
27	Operation	operator: 38 operands: 37
28	Operation	operator: 38 operands: 39
29	Lambda	parameter: 48 body: 40
30	Variable
31	Lambda	parameter: 48 body: 41
32	Variable
33	Lambda	parameter: 48 body: 42
34	Literal
35	Variable
36	ExprTuple	40, 43
37	ExprTuple	41, 43
38	Literal
39	ExprTuple	42, 43
40	IndexedVar	variable: 44 index: 48
41	IndexedVar	variable: 45 index: 48
42	IndexedVar	variable: 46 index: 48
43	Literal
44	Variable
45	Variable
46	Variable
47	ExprTuple	48
48	Variable