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, ExprRange, IndexedVar, Variable, a, b, c, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, InSet
from proveit.numbers import Add, Less, RealNeg, RealNonPos, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(Add(a_1_to_i, b, c_1_to_j), RealNeg), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RealNonPos), one, i), InSet(b, RealNonPos), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), RealNonPos), one, j), Less(b, zero)))

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_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \in \mathbb{R}^- \textrm{ if } \left(a_{1} \in \mathbb{R}^{\le 0}\right) ,  \left(a_{2} \in \mathbb{R}^{\le 0}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{R}^{\le 0}\right) ,  b \in \mathbb{R}^{\le 0}, \left(c_{1} \in \mathbb{R}^{\le 0}\right) ,  \left(c_{2} \in \mathbb{R}^{\le 0}\right) ,  \ldots ,  \left(c_{j} \in \mathbb{R}^{\le 0}\right) ,  b < 0\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: 31 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10, 11
6	Operation	operator: 12 operands: 13
7	Literal
8	ExprRange	lambda_map: 14 start_index: 28 end_index: 26
9	Operation	operator: 31 operands: 15
10	ExprRange	lambda_map: 16 start_index: 28 end_index: 29
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19, 23, 20
14	Lambda	parameter: 39 body: 21
15	ExprTuple	23, 35
16	Lambda	parameter: 39 body: 22
17	Literal
18	ExprTuple	23, 24
19	ExprRange	lambda_map: 25 start_index: 28 end_index: 26
20	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
21	Operation	operator: 31 operands: 30
22	Operation	operator: 31 operands: 32
23	Variable
24	Literal
25	Lambda	parameter: 39 body: 33
26	Variable
27	Lambda	parameter: 39 body: 34
28	Literal
29	Variable
30	ExprTuple	33, 35
31	Literal
32	ExprTuple	34, 35
33	IndexedVar	variable: 36 index: 39
34	IndexedVar	variable: 37 index: 39
35	Literal
36	Variable
37	Variable
38	ExprTuple	39
39	Variable