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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, Real, one, zero
from proveit.numbers.exponentiation import prod_ai_raise_b__1_to_m

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = ExprTuple(Lambda([a_1_to_m, b], Conditional(Equals(Exp(Mult(a_1_to_m), b), prod_ai_raise_b__1_to_m), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, m), InSet(b, Real), ExprRange(sub_expr1, NotEquals(sub_expr2, zero), one, m)))))

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(a_{1}, a_{2}, \ldots, a_{m}, b\right) \mapsto \left\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{m}\right)^{b} = \left(\left(a_{1}\right)^{b} \cdot  \left(a_{2}\right)^{b} \cdot  \ldots \cdot  \left(a_{m}\right)^{b}\right) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{m} \in \mathbb{C}\right) ,  b \in \mathbb{R}, \left(a_{1} \neq 0\right) ,  \left(a_{2} \neq 0\right) ,  \ldots ,  \left(a_{m} \neq 0\right)\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	32, 42
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 39 operands: 15
11	Operation	operator: 25 operands: 16
12	ExprRange	lambda_map: 17 start_index: 37 end_index: 38
13	Operation	operator: 28 operands: 18
14	ExprRange	lambda_map: 19 start_index: 37 end_index: 38
15	ExprTuple	20, 42
16	ExprTuple	21
17	Lambda	parameter: 45 body: 22
18	ExprTuple	42, 23
19	Lambda	parameter: 45 body: 24
20	Operation	operator: 25 operands: 26
21	ExprRange	lambda_map: 27 start_index: 37 end_index: 38
22	Operation	operator: 28 operands: 29
23	Literal
24	Operation	operator: 30 operands: 31
25	Literal
26	ExprTuple	32
27	Lambda	parameter: 45 body: 33
28	Literal
29	ExprTuple	41, 34
30	Literal
31	ExprTuple	41, 35
32	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
33	Operation	operator: 39 operands: 40
34	Literal
35	Literal
36	Lambda	parameter: 45 body: 41
37	Literal
38	Variable
39	Literal
40	ExprTuple	41, 42
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable