Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([a_1_to_i, b, c_1_to_j], 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) \mapsto \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..\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	parameters: 15 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 33 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12, 13
8	Operation	operator: 14 operands: 15
9	Literal
10	ExprRange	lambda_map: 16 start_index: 30 end_index: 28
11	Operation	operator: 33 operands: 17
12	ExprRange	lambda_map: 18 start_index: 30 end_index: 31
13	Operation	operator: 19 operands: 20
14	Literal
15	ExprTuple	21, 25, 22
16	Lambda	parameter: 41 body: 23
17	ExprTuple	25, 37
18	Lambda	parameter: 41 body: 24
19	Literal
20	ExprTuple	25, 26
21	ExprRange	lambda_map: 27 start_index: 30 end_index: 28
22	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
23	Operation	operator: 33 operands: 32
24	Operation	operator: 33 operands: 34
25	Variable
26	Literal
27	Lambda	parameter: 41 body: 35
28	Variable
29	Lambda	parameter: 41 body: 36
30	Literal
31	Variable
32	ExprTuple	35, 37
33	Literal
34	ExprTuple	36, 37
35	IndexedVar	variable: 38 index: 41
36	IndexedVar	variable: 39 index: 41
37	Literal
38	Variable
39	Variable
40	ExprTuple	41
41	Variable