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, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import Add, Complex, Mult, Natural

# build up the expression from sub-expressions
expr = Lambda([n, x], Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Equals(Add(a_1_to_n), Mult(x, n)), domain = Set(x)), And(InSet(n, Natural), InSet(x, 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(n, x\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in \left\{x\right\}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{n}\right) = \left(x \cdot n\right)\right) \textrm{ if } n \in \mathbb{N} ,  x \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: 1 body: 2
1	ExprTuple	34, 44
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 20 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 26 body: 11
9	Operation	operator: 35 operands: 12
10	Operation	operator: 35 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	34, 16
13	ExprTuple	44, 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	ExprRange	lambda_map: 29 start_index: 33 end_index: 34
25	Literal
26	ExprTuple	30
27	Literal
28	ExprTuple	44, 34
29	Lambda	parameter: 43 body: 31
30	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
31	Operation	operator: 35 operands: 36
32	Lambda	parameter: 43 body: 37
33	Literal
34	Variable
35	Literal
36	ExprTuple	37, 38
37	IndexedVar	variable: 39 index: 43
38	Operation	operator: 41 operand: 44
39	Variable
40	ExprTuple	43
41	Literal
42	ExprTuple	44
43	Variable
44	Variable