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, k, m
from proveit.core_expr_types import k_1_to_m
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Exp, NaturalPos, one
from proveit.numbers.exponentiation import prod_a_raise_ki__1_to_m

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a, k_1_to_m], Conditional(Equals(prod_a_raise_ki__1_to_m, Exp(a, Add(k_1_to_m))), And(InSet(a, Complex), ExprRange(sub_expr1, InSet(IndexedVar(k, sub_expr1), NaturalPos), 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, k_{1}, k_{2}, \ldots, k_{m}\right) \mapsto \left\{\left(a^{k_{1}} \cdot  a^{k_{2}} \cdot  \ldots \cdot  a^{k_{m}}\right) = a^{k_{1} +  k_{2} +  \ldots +  k_{m}} \textrm{ if } a \in \mathbb{C}, \left(k_{1} \in \mathbb{N}^+\right) ,  \left(k_{2} \in \mathbb{N}^+\right) ,  \ldots ,  \left(k_{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	Lambda	parameters: 1 body: 2
1	ExprTuple	35, 28
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: 13 operands: 14
10	Operation	operator: 30 operands: 15
11	Operation	operator: 25 operands: 16
12	ExprRange	lambda_map: 17 start_index: 33 end_index: 34
13	Literal
14	ExprTuple	18
15	ExprTuple	35, 19
16	ExprTuple	35, 20
17	Lambda	parameter: 39 body: 21
18	ExprRange	lambda_map: 22 start_index: 33 end_index: 34
19	Operation	operator: 23 operands: 24
20	Literal
21	Operation	operator: 25 operands: 26
22	Lambda	parameter: 39 body: 27
23	Literal
24	ExprTuple	28
25	Literal
26	ExprTuple	36, 29
27	Operation	operator: 30 operands: 31
28	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
29	Literal
30	Literal
31	ExprTuple	35, 36
32	Lambda	parameter: 39 body: 36
33	Literal
34	Variable
35	Variable
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable