Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	35, 45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 27 body: 12
10	Operation	operator: 36 operands: 13
11	Operation	operator: 36 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	35, 17
14	ExprTuple	45, 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprRange	lambda_map: 30 start_index: 34 end_index: 35
26	Literal
27	ExprTuple	31
28	Literal
29	ExprTuple	45, 35
30	Lambda	parameter: 44 body: 32
31	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
32	Operation	operator: 36 operands: 37
33	Lambda	parameter: 44 body: 38
34	Literal
35	Variable
36	Literal
37	ExprTuple	38, 39
38	IndexedVar	variable: 40 index: 44
39	Operation	operator: 42 operand: 45
40	Variable
41	ExprTuple	44
42	Literal
43	ExprTuple	45
44	Variable
45	Variable