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, Neg, 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, Neg(b)), n), Exp(a, Neg(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^{-\left(b \cdot n\right)}\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: 45 body: 2
1	ExprTuple	45
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 26 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	45, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	37, 44
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 34 operands: 23
19	Operation	operator: 34 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 28 operands: 29
23	ExprTuple	30, 45
24	ExprTuple	37, 31
25	ExprTuple	37, 32
26	Literal
27	ExprTuple	44, 32
28	Literal
29	ExprTuple	37, 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 40 operand: 39
32	Literal
33	Literal
34	Literal
35	ExprTuple	37, 38
36	ExprTuple	39
37	Variable
38	Operation	operator: 40 operand: 44
39	Operation	operator: 42 operands: 43
40	Literal
41	ExprTuple	44
42	Literal
43	ExprTuple	44, 45
44	Variable
45	Variable