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, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos, RealPos
from proveit.numbers.exponentiation import prod_ai_raise_b__1_to_m

# build up the expression from sub-expressions
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 = [RealPos, Complex]), 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{R}^+\right), \left(a_{2} \in \mathbb{R}^+\right), \ldots, \left(a_{m} \in \mathbb{R}^+\right), b \in \mathbb{C}}~\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: 41 body: 3
2	ExprTuple	41
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 34 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	41, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	36, 45
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
19	Operation	operator: 42 operands: 23
20	Operation	operator: 31 operands: 24
21	ExprRange	lambda_map: 25 start_index: 40 end_index: 41
22	Operation	operator: 34 operands: 26
23	ExprTuple	27, 45
24	ExprTuple	28
25	Lambda	parameter: 48 body: 29
26	ExprTuple	45, 30
27	Operation	operator: 31 operands: 32
28	ExprRange	lambda_map: 33 start_index: 40 end_index: 41
29	Operation	operator: 34 operands: 35
30	Literal
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