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, NotEquals
from proveit.numbers import Complex, Exp, Mult, Neg, zero

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Exp(Exp(a, Neg(b)), n), Exp(a, Neg(Mult(b, n)))), And(InSet(a, Complex), InSet(b, Complex), 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\right) \mapsto \left\{(a^{-b})^{n} = a^{-\left(b \cdot n\right)} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  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	28, 35
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: 25 operands: 14
10	Operation	operator: 25 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 19 operands: 20
14	ExprTuple	21, 36
15	ExprTuple	28, 22
16	ExprTuple	28, 23
17	Literal
18	ExprTuple	35, 23
19	Literal
20	ExprTuple	28, 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 31 operand: 30
23	Literal
24	Literal
25	Literal
26	ExprTuple	28, 29
27	ExprTuple	30
28	Variable
29	Operation	operator: 31 operand: 35
30	Operation	operator: 33 operands: 34
31	Literal
32	ExprTuple	35
33	Literal
34	ExprTuple	35, 36
35	Variable
36	Variable