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 Equals, Forall, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, NaturalPos, 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}")
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [a_1_to_m, b], instance_expr = Equals(Exp(Mult(a_1_to_m), b), prod_ai_raise_b__1_to_m), domains = [Complex, Real], condition = ExprRange(sub_expr1, NotEquals(IndexedVar(a, sub_expr1), zero), one, m)), InSet(m, 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(m \mapsto \left\{\forall_{\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)}~\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)\right) \textrm{ if } m \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	parameter: 47 body: 3
2	ExprTuple	47
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 37 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	47, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	41, 51
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23
19	Operation	operator: 48 operands: 24
20	Operation	operator: 34 operands: 25
21	ExprRange	lambda_map: 26 start_index: 46 end_index: 47
22	Operation	operator: 37 operands: 27
23	ExprRange	lambda_map: 28 start_index: 46 end_index: 47
24	ExprTuple	29, 51
25	ExprTuple	30
26	Lambda	parameter: 54 body: 31
27	ExprTuple	51, 32
28	Lambda	parameter: 54 body: 33
29	Operation	operator: 34 operands: 35
30	ExprRange	lambda_map: 36 start_index: 46 end_index: 47
31	Operation	operator: 37 operands: 38
32	Literal
33	Operation	operator: 39 operands: 40
34	Literal
35	ExprTuple	41
36	Lambda	parameter: 54 body: 42
37	Literal
38	ExprTuple	50, 43
39	Literal
40	ExprTuple	50, 44
41	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
42	Operation	operator: 48 operands: 49
43	Literal
44	Literal
45	Lambda	parameter: 54 body: 50
46	Literal
47	Variable
48	Literal
49	ExprTuple	50, 51
50	IndexedVar	variable: 52 index: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable