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(Mult(a_1_to_i, Neg(b), c_1_to_j), Neg(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(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) = \left(-\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)\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: 23 operands: 12
8	Operation	operator: 21 operand: 18
9	ExprRange	lambda_map: 14 start_index: 35 end_index: 33
10	Operation	operator: 26 operands: 15
11	ExprRange	lambda_map: 16 start_index: 35 end_index: 36
12	ExprTuple	28, 17, 30
13	ExprTuple	18
14	Lambda	parameter: 42 body: 19
15	ExprTuple	29, 31
16	Lambda	parameter: 42 body: 20
17	Operation	operator: 21 operand: 29
18	Operation	operator: 23 operands: 24
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	Literal
22	ExprTuple	29
23	Literal
24	ExprTuple	28, 29, 30
25	ExprTuple	37, 31
26	Literal
27	ExprTuple	38, 31
28	ExprRange	lambda_map: 32 start_index: 35 end_index: 33
29	Variable
30	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
31	Literal
32	Lambda	parameter: 42 body: 37
33	Variable
34	Lambda	parameter: 42 body: 38
35	Literal
36	Variable
37	IndexedVar	variable: 39 index: 42
38	IndexedVar	variable: 40 index: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable