Expression of type ExprTuple

from the theory of proveit.numbers.exponentiation

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, m, n
from proveit.core_expr_types import a_1_to_m
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos
from proveit.numbers.exponentiation import prod_ai_raise_n__1_to_m

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [a_1_to_m], instance_expr = Equals(Exp(Mult(a_1_to_m), n), prod_ai_raise_n__1_to_m), domain = Complex), And(InSet(m, NaturalPos), InSet(n, 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())

\left(\left(m, n\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m} \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{m}\right)^{n} = \left(\left(a_{1}\right)^{n} \cdot  \left(a_{2}\right)^{n} \cdot  \ldots \cdot  \left(a_{m}\right)^{n}\right)\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\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	41, 45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 32 body: 12
10	Operation	operator: 34 operands: 13
11	Operation	operator: 34 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	41, 17
14	ExprTuple	45, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24
22	Operation	operator: 42 operands: 25
23	Operation	operator: 31 operands: 26
24	ExprRange	lambda_map: 27 start_index: 40 end_index: 41
25	ExprTuple	28, 45
26	ExprTuple	29
27	Lambda	parameter: 48 body: 30
28	Operation	operator: 31 operands: 32
29	ExprRange	lambda_map: 33 start_index: 40 end_index: 41
30	Operation	operator: 34 operands: 35
31	Literal
32	ExprTuple	36
33	Lambda	parameter: 48 body: 37
34	Literal
35	ExprTuple	44, 38
36	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
37	Operation	operator: 42 operands: 43
38	Literal
39	Lambda	parameter: 48 body: 44
40	Literal
41	Variable
42	Literal
43	ExprTuple	44, 45
44	IndexedVar	variable: 46 index: 48
45	Variable
46	Variable
47	ExprTuple	48
48	Variable