Expression of type Conditional

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, IndexedVar, Variable, a, b, c, d, i, j, k
from proveit.core_expr_types import a_1_to_i, b_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 = Conditional(Equals(Mult(a_1_to_i, b_1_to_j, c, d_1_to_k), Mult(a_1_to_i, c, b_1_to_j, d_1_to_k)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j), InSet(c, Complex), 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\{\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j} \cdot c\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\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\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), \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{j} \in \mathbb{C}\right) ,  c \in \mathbb{C}, \left(d_{1} \in \mathbb{C}\right) ,  \left(d_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(d_{k} \in \mathbb{C}\right)\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11, 12
7	Operation	operator: 14 operands: 13
8	Operation	operator: 14 operands: 15
9	ExprRange	lambda_map: 16 start_index: 32 end_index: 28
10	ExprRange	lambda_map: 17 start_index: 32 end_index: 30
11	Operation	operator: 36 operands: 18
12	ExprRange	lambda_map: 19 start_index: 32 end_index: 33
13	ExprTuple	20, 21, 25, 22
14	Literal
15	ExprTuple	20, 25, 21, 22
16	Lambda	parameter: 46 body: 23
17	Lambda	parameter: 46 body: 24
18	ExprTuple	25, 41
19	Lambda	parameter: 46 body: 26
20	ExprRange	lambda_map: 27 start_index: 32 end_index: 28
21	ExprRange	lambda_map: 29 start_index: 32 end_index: 30
22	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
23	Operation	operator: 36 operands: 34
24	Operation	operator: 36 operands: 35
25	Variable
26	Operation	operator: 36 operands: 37
27	Lambda	parameter: 46 body: 38
28	Variable
29	Lambda	parameter: 46 body: 39
30	Variable
31	Lambda	parameter: 46 body: 40
32	Literal
33	Variable
34	ExprTuple	38, 41
35	ExprTuple	39, 41
36	Literal
37	ExprTuple	40, 41
38	IndexedVar	variable: 42 index: 46
39	IndexedVar	variable: 43 index: 46
40	IndexedVar	variable: 44 index: 46
41	Literal
42	Variable
43	Variable
44	Variable
45	ExprTuple	46
46	Variable