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, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
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, one, b_1_to_j), Mult(a_1_to_i, b_1_to_j)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, 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 1\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) = \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{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), \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{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
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprRange	lambda_map: 14 start_index: 23 end_index: 21
10	ExprRange	lambda_map: 15 start_index: 23 end_index: 24
11	ExprTuple	16, 23, 17
12	Literal
13	ExprTuple	16, 17
14	Lambda	parameter: 34 body: 18
15	Lambda	parameter: 34 body: 19
16	ExprRange	lambda_map: 20 start_index: 23 end_index: 21
17	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
18	Operation	operator: 26 operands: 25
19	Operation	operator: 26 operands: 27
20	Lambda	parameter: 34 body: 28
21	Variable
22	Lambda	parameter: 34 body: 29
23	Literal
24	Variable
25	ExprTuple	28, 30
26	Literal
27	ExprTuple	29, 30
28	IndexedVar	variable: 31 index: 34
29	IndexedVar	variable: 32 index: 34
30	Literal
31	Variable
32	Variable
33	ExprTuple	34
34	Variable