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 Equals, Forall, InSet, Or
from proveit.numbers import Complex, Mult, Natural, ZeroSet, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Mult(a_1_to_n), ZeroSet), domain = Complex, condition = Or(ExprRange(sub_expr1, Equals(IndexedVar(a, sub_expr1), zero), one, n))), InSet(n, Natural))

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\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{C}~|~\left(a_{1} = 0\right) \lor  \left(a_{2} = 0\right) \lor  \ldots \lor  \left(a_{n} = 0\right)}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \in \left\{0\right\}\right) \textrm{ if } n \in \mathbb{N}\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 operand: 6
2	Operation	operator: 29 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	33, 7
6	Lambda	parameters: 19 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 29 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operand: 39
16	ExprRange	lambda_map: 22 start_index: 32 end_index: 33
17	Operation	operator: 23 operands: 24
18	Literal
19	ExprTuple	25
20	Literal
21	ExprTuple	39
22	Lambda	parameter: 42 body: 26
23	Literal
24	ExprTuple	27
25	ExprRange	lambda_map: 28 start_index: 32 end_index: 33
26	Operation	operator: 29 operands: 30
27	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
28	Lambda	parameter: 42 body: 38
29	Literal
30	ExprTuple	38, 34
31	Lambda	parameter: 42 body: 35
32	Literal
33	Variable
34	Literal
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	IndexedVar	variable: 40 index: 42
39	Literal
40	Variable
41	ExprTuple	42
42	Variable