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, 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 = 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(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..

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	31, 41
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, 13
9	Operation	operator: 38 operands: 14
10	Operation	operator: 24 operands: 15
11	ExprRange	lambda_map: 16 start_index: 36 end_index: 37
12	Operation	operator: 27 operands: 17
13	ExprRange	lambda_map: 18 start_index: 36 end_index: 37
14	ExprTuple	19, 41
15	ExprTuple	20
16	Lambda	parameter: 44 body: 21
17	ExprTuple	41, 22
18	Lambda	parameter: 44 body: 23
19	Operation	operator: 24 operands: 25
20	ExprRange	lambda_map: 26 start_index: 36 end_index: 37
21	Operation	operator: 27 operands: 28
22	Literal
23	Operation	operator: 29 operands: 30
24	Literal
25	ExprTuple	31
26	Lambda	parameter: 44 body: 32
27	Literal
28	ExprTuple	40, 33
29	Literal
30	ExprTuple	40, 34
31	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
32	Operation	operator: 38 operands: 39
33	Literal
34	Literal
35	Lambda	parameter: 44 body: 40
36	Literal
37	Variable
38	Literal
39	ExprTuple	40, 41
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable