Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([a_1_to_n], 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}, a_{2}, \ldots, a_{n}\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 13 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 23 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operand: 33
10	ExprRange	lambda_map: 16 start_index: 26 end_index: 27
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19
14	Literal
15	ExprTuple	33
16	Lambda	parameter: 36 body: 20
17	Literal
18	ExprTuple	21
19	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
20	Operation	operator: 23 operands: 24
21	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
22	Lambda	parameter: 36 body: 32
23	Literal
24	ExprTuple	32, 28
25	Lambda	parameter: 36 body: 29
26	Literal
27	Variable
28	Literal
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	IndexedVar	variable: 34 index: 36
33	Literal
34	Variable
35	ExprTuple	36
36	Variable