Expression of type Lambda

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, IndexedVar, Lambda, Variable, a, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, RealPos, one
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 = 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(IndexedVar(a, sub_expr1), RealPos), one, m), InSet(b, 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(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{R}^+\right) ,  \left(a_{2} \in \mathbb{R}^+\right) ,  \ldots ,  \left(a_{m} \in \mathbb{R}^+\right) ,  b \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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