Expression of type Conditional

from the theory of proveit.numbers.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.logic import Forall, InSet
from proveit.numbers import Add, IntegerNonPos, Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(Add(a_1_to_i), IntegerNonPos), domain = IntegerNonPos), InSet(i, 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_{i} \in \mathbb{Z}^{\leq 0}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \in \mathbb{Z}^{\leq 0}\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: 24 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	23, 7
6	Lambda	parameters: 17 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 24 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 27
12	Literal
13	ExprTuple	15
14	Operation	operator: 16 operands: 17
15	ExprRange	lambda_map: 18 start_index: 22 end_index: 23
16	Literal
17	ExprTuple	19
18	Lambda	parameter: 30 body: 20
19	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
20	Operation	operator: 24 operands: 25
21	Lambda	parameter: 30 body: 26
22	Literal
23	Variable
24	Literal
25	ExprTuple	26, 27
26	IndexedVar	variable: 28 index: 30
27	Literal
28	Variable
29	ExprTuple	30
30	Variable