Expression of type Lambda

from the theory of proveit.numbers.multiplication

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, b, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n, b], instance_expr = Equals(Mult(a_1_to_n, b), Mult(Mult(a_1_to_n), b)), domain = Complex), InSet(n, 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())

n \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{n}, b \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n} \cdot b\right) = \left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \cdot b\right)\right) \textrm{ if } n \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: 36 body: 2
1	ExprTuple	36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 30 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	36, 9
8	Lambda	parameters: 21 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, 20
17	Operation	operator: 28 operands: 21
18	Operation	operator: 28 operands: 22
19	ExprRange	lambda_map: 23 start_index: 35 end_index: 36
20	Operation	operator: 30 operands: 24
21	ExprTuple	32, 27
22	ExprTuple	25, 27
23	Lambda	parameter: 40 body: 26
24	ExprTuple	27, 33
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Variable
28	Literal
29	ExprTuple	32
30	Literal
31	ExprTuple	37, 33
32	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
33	Literal
34	Lambda	parameter: 40 body: 37
35	Literal
36	Variable
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable