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, Lambda, i
from proveit.core_expr_types import a_1_to_i
from proveit.logic import Forall, InSet
from proveit.numbers import Add, Natural, RealNonPos

# build up the expression from sub-expressions
expr = Lambda(i, Conditional(Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(Add(a_1_to_i), RealNonPos), domain = RealNonPos), 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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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