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 b_1_to_m
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, Real, one, zero
from proveit.numbers.exponentiation import prod_a_raise_bi__1_to_m

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a, b_1_to_m], Conditional(Equals(prod_a_raise_bi__1_to_m, Exp(a, Add(b_1_to_m))), And(InSet(a, Complex), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Real), one, m), NotEquals(a, zero))))

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, b_{1}, b_{2}, \ldots, b_{m}\right) \mapsto \left\{\left(a^{b_{1}} \cdot  a^{b_{2}} \cdot  \ldots \cdot  a^{b_{m}}\right) = a^{b_{1} +  b_{2} +  \ldots +  b_{m}} \textrm{ if } a \in \mathbb{C}, \left(b_{1} \in \mathbb{R}\right) ,  \left(b_{2} \in \mathbb{R}\right) ,  \ldots ,  \left(b_{m} \in \mathbb{R}\right) ,  a \neq 0\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	39, 32
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: 14 operands: 15
10	Operation	operator: 34 operands: 16
11	Operation	operator: 29 operands: 17
12	ExprRange	lambda_map: 18 start_index: 37 end_index: 38
13	Operation	operator: 19 operands: 20
14	Literal
15	ExprTuple	21
16	ExprTuple	39, 22
17	ExprTuple	39, 23
18	Lambda	parameter: 43 body: 24
19	Literal
20	ExprTuple	39, 25
21	ExprRange	lambda_map: 26 start_index: 37 end_index: 38
22	Operation	operator: 27 operands: 28
23	Literal
24	Operation	operator: 29 operands: 30
25	Literal
26	Lambda	parameter: 43 body: 31
27	Literal
28	ExprTuple	32
29	Literal
30	ExprTuple	40, 33
31	Operation	operator: 34 operands: 35
32	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
33	Literal
34	Literal
35	ExprTuple	39, 40
36	Lambda	parameter: 43 body: 40
37	Literal
38	Variable
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable