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 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 = ExprTuple(Lambda(n, 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(n \mapsto \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..\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	parameter: 36 body: 3
2	ExprTuple	36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 32 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	36, 10
9	Lambda	parameters: 22 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 32 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operand: 42
19	ExprRange	lambda_map: 25 start_index: 35 end_index: 36
20	Operation	operator: 26 operands: 27
21	Literal
22	ExprTuple	28
23	Literal
24	ExprTuple	42
25	Lambda	parameter: 45 body: 29
26	Literal
27	ExprTuple	30
28	ExprRange	lambda_map: 31 start_index: 35 end_index: 36
29	Operation	operator: 32 operands: 33
30	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
31	Lambda	parameter: 45 body: 41
32	Literal
33	ExprTuple	41, 37
34	Lambda	parameter: 45 body: 38
35	Literal
36	Variable
37	Literal
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	IndexedVar	variable: 43 index: 45
42	Literal
43	Variable
44	ExprTuple	45
45	Variable