Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 14 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 32 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11, 12
7	Operation	operator: 13 operands: 14
8	Literal
9	ExprRange	lambda_map: 15 start_index: 29 end_index: 27
10	Operation	operator: 32 operands: 16
11	ExprRange	lambda_map: 17 start_index: 29 end_index: 30
12	Operation	operator: 18 operands: 19
13	Literal
14	ExprTuple	20, 24, 21
15	Lambda	parameter: 40 body: 22
16	ExprTuple	24, 36
17	Lambda	parameter: 40 body: 23
18	Literal
19	ExprTuple	24, 25
20	ExprRange	lambda_map: 26 start_index: 29 end_index: 27
21	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
22	Operation	operator: 32 operands: 31
23	Operation	operator: 32 operands: 33
24	Variable
25	Literal
26	Lambda	parameter: 40 body: 34
27	Variable
28	Lambda	parameter: 40 body: 35
29	Literal
30	Variable
31	ExprTuple	34, 36
32	Literal
33	ExprTuple	35, 36
34	IndexedVar	variable: 37 index: 40
35	IndexedVar	variable: 38 index: 40
36	Literal
37	Variable
38	Variable
39	ExprTuple	40
40	Variable