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, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, Neg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Neg(Mult(a_1_to_i, Neg(b), c_1_to_j)), Mult(a_1_to_i, b, c_1_to_j)), 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)))

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(-\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(-b\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right)\right) = \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right) \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)\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
7	Operation	operator: 31 operand: 17
8	Operation	operator: 20 operands: 13
9	ExprRange	lambda_map: 14 start_index: 34 end_index: 30
10	Operation	operator: 23 operands: 15
11	ExprRange	lambda_map: 16 start_index: 34 end_index: 35
12	ExprTuple	17
13	ExprTuple	25, 37, 27
14	Lambda	parameter: 42 body: 18
15	ExprTuple	37, 28
16	Lambda	parameter: 42 body: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 23 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	ExprTuple	25, 26, 27
22	ExprTuple	36, 28
23	Literal
24	ExprTuple	38, 28
25	ExprRange	lambda_map: 29 start_index: 34 end_index: 30
26	Operation	operator: 31 operand: 37
27	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
28	Literal
29	Lambda	parameter: 42 body: 36
30	Variable
31	Literal
32	ExprTuple	37
33	Lambda	parameter: 42 body: 38
34	Literal
35	Variable
36	IndexedVar	variable: 39 index: 42
37	Variable
38	IndexedVar	variable: 40 index: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable