Expression of type Lambda

from the theory of proveit.linear_algebra.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.linear_algebra import VecAdd
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Complex, NaturalPos

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

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{C}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}\right)\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: 28 body: 2
1	ExprTuple	28
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 29 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	28, 9
8	Lambda	parameters: 22 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 22
18	Operation	operator: 21 operands: 22
19	ExprRange	lambda_map: 23 start_index: 27 end_index: 28
20	Literal
21	Literal
22	ExprTuple	24
23	Lambda	parameter: 35 body: 25
24	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
25	Operation	operator: 29 operands: 30
26	Lambda	parameter: 35 body: 31
27	Literal
28	Variable
29	Literal
30	ExprTuple	31, 32
31	IndexedVar	variable: 33 index: 35
32	Literal
33	Variable
34	ExprTuple	35
35	Variable