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, ExprRange, IndexedVar, Lambda, Variable, a, b, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_n, b], Conditional(Equals(Mult(a_1_to_n, b), Mult(Mult(a_1_to_n), b)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, n), InSet(b, Complex))))

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_{n}, b\right) \mapsto \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) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{n} \in \mathbb{C}\right) ,  b \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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