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, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, Equals, InSet, Or
from proveit.numbers import Complex, Mult, ZeroSet, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = Conditional(InSet(Mult(a_1_to_n), ZeroSet), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, n), Or(ExprRange(sub_expr1, Equals(sub_expr2, zero), one, n))))

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_{n}\right) \in \left\{0\right\} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{n} \in \mathbb{C}\right) ,  \left(a_{1} = 0\right) \lor  \left(a_{2} = 0\right) \lor  \ldots \lor  \left(a_{n} = 0\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: 21 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 10 operands: 11
7	Operation	operator: 12 operand: 31
8	ExprRange	lambda_map: 14 start_index: 24 end_index: 25
9	Operation	operator: 15 operands: 16
10	Literal
11	ExprTuple	17
12	Literal
13	ExprTuple	31
14	Lambda	parameter: 34 body: 18
15	Literal
16	ExprTuple	19
17	ExprRange	lambda_map: 20 start_index: 24 end_index: 25
18	Operation	operator: 21 operands: 22
19	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
20	Lambda	parameter: 34 body: 30
21	Literal
22	ExprTuple	30, 26
23	Lambda	parameter: 34 body: 27
24	Literal
25	Variable
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	IndexedVar	variable: 32 index: 34
31	Literal
32	Variable
33	ExprTuple	34
34	Variable