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 Equals, Forall, InSet, NotEquals
from proveit.numbers import Complex, Exp, Integer, Mult, zero

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Exp(Exp(a, b), n), Exp(a, Mult(b, n))), domain = Complex, condition = NotEquals(a, zero)), InSet(n, Integer)))

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())

n \mapsto \left\{\forall_{a, b \in \mathbb{C}~|~a \neq 0}~\left((a^{b})^{n} = a^{b \cdot n}\right) \textrm{ if } n \in \mathbb{Z}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 39 body: 2
1	ExprTuple	39
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 25 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	39, 9
8	Lambda	parameters: 34 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20, 21
17	Operation	operator: 33 operands: 22
18	Operation	operator: 33 operands: 23
19	Operation	operator: 25 operands: 24
20	Operation	operator: 25 operands: 26
21	Operation	operator: 27 operands: 28
22	ExprTuple	29, 39
23	ExprTuple	37, 30
24	ExprTuple	37, 31
25	Literal
26	ExprTuple	38, 31
27	Literal
28	ExprTuple	37, 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operands: 36
31	Literal
32	Literal
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Variable
39	Variable