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, a, b, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos

# build up the expression from sub-expressions
expr = Lambda([a, b, n], Conditional(Equals(Exp(Mult(a, b), n), Mult(Exp(a, n), Exp(b, n))), And(InSet(a, Complex), InSet(b, Complex), 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(a, b, n\right) \mapsto \left\{\left(a \cdot b\right)^{n} = \left(a^{n} \cdot b^{n}\right) \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  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	30, 31, 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: 28 operands: 14
10	Operation	operator: 25 operands: 15
11	Operation	operator: 18 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	20, 32
15	ExprTuple	21, 22
16	ExprTuple	30, 23
17	ExprTuple	31, 23
18	Literal
19	ExprTuple	32, 24
20	Operation	operator: 25 operands: 26
21	Operation	operator: 28 operands: 27
22	Operation	operator: 28 operands: 29
23	Literal
24	Literal
25	Literal
26	ExprTuple	30, 31
27	ExprTuple	30, 32
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Variable
32	Variable