Expression of type Conditional

from the theory of proveit.linear_algebra.addition

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, i
from proveit.core_expr_types import a_1_to_i
from proveit.linear_algebra import VecAdd
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Complex, NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i], instance_expr = Equals(VecAdd(a_1_to_i), Add(a_1_to_i)), domain = Complex), InSet(i, NaturalPos))

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