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, i
from proveit.core_expr_types import a_1_to_i
from proveit.logic import And, InSet
from proveit.numbers import Add, RealNonPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i], Conditional(InSet(Add(a_1_to_i), RealNonPos), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RealNonPos), one, i))))

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}\right) \mapsto \left\{\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \in \mathbb{R}^{\le 0} \textrm{ if } \left(a_{1} \in \mathbb{R}^{\le 0}\right) \land  \left(a_{2} \in \mathbb{R}^{\le 0}\right) \land  \ldots \land  \left(a_{i} \in \mathbb{R}^{\le 0}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 10 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 17 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 20
5	Literal
6	ExprTuple	8
7	Operation	operator: 9 operands: 10
8	ExprRange	lambda_map: 11 start_index: 15 end_index: 16
9	Literal
10	ExprTuple	12
11	Lambda	parameter: 23 body: 13
12	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
13	Operation	operator: 17 operands: 18
14	Lambda	parameter: 23 body: 19
15	Literal
16	Variable
17	Literal
18	ExprTuple	19, 20
19	IndexedVar	variable: 21 index: 23
20	Literal
21	Variable
22	ExprTuple	23
23	Variable