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, Lambda, m, n
from proveit.core_expr_types import a_1_to_m
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos
from proveit.numbers.exponentiation import prod_ai_raise_n__1_to_m

# build up the expression from sub-expressions
expr = Lambda([m, n], Conditional(Forall(instance_param_or_params = [a_1_to_m], instance_expr = Equals(Exp(Mult(a_1_to_m), n), prod_ai_raise_n__1_to_m), domain = Complex), And(InSet(m, NaturalPos), InSet(n, 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, n\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m} \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{m}\right)^{n} = \left(\left(a_{1}\right)^{n} \cdot  \left(a_{2}\right)^{n} \cdot  \ldots \cdot  \left(a_{m}\right)^{n}\right)\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\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	40, 44
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 31 body: 11
9	Operation	operator: 33 operands: 12
10	Operation	operator: 33 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	40, 16
13	ExprTuple	44, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23
21	Operation	operator: 41 operands: 24
22	Operation	operator: 30 operands: 25
23	ExprRange	lambda_map: 26 start_index: 39 end_index: 40
24	ExprTuple	27, 44
25	ExprTuple	28
26	Lambda	parameter: 47 body: 29
27	Operation	operator: 30 operands: 31
28	ExprRange	lambda_map: 32 start_index: 39 end_index: 40
29	Operation	operator: 33 operands: 34
30	Literal
31	ExprTuple	35
32	Lambda	parameter: 47 body: 36
33	Literal
34	ExprTuple	43, 37
35	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
36	Operation	operator: 41 operands: 42
37	Literal
38	Lambda	parameter: 47 body: 43
39	Literal
40	Variable
41	Literal
42	ExprTuple	43, 44
43	IndexedVar	variable: 45 index: 47
44	Variable
45	Variable
46	ExprTuple	47
47	Variable