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, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Mult(a_1_to_i, zero, b_1_to_j), zero), 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 0\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) = 0 \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, 15
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 11
8	ExprRange	lambda_map: 12 start_index: 22 end_index: 20
9	ExprRange	lambda_map: 13 start_index: 22 end_index: 23
10	Literal
11	ExprTuple	14, 15, 16
12	Lambda	parameter: 33 body: 17
13	Lambda	parameter: 33 body: 18
14	ExprRange	lambda_map: 19 start_index: 22 end_index: 20
15	Literal
16	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
17	Operation	operator: 25 operands: 24
18	Operation	operator: 25 operands: 26
19	Lambda	parameter: 33 body: 27
20	Variable
21	Lambda	parameter: 33 body: 28
22	Literal
23	Variable
24	ExprTuple	27, 29
25	Literal
26	ExprTuple	28, 29
27	IndexedVar	variable: 30 index: 33
28	IndexedVar	variable: 31 index: 33
29	Literal
30	Variable
31	Variable
32	ExprTuple	33
33	Variable