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)), Neg(n)), Exp(a, 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^{b \cdot n} \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	31, 36
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: 26 operands: 14
10	Operation	operator: 26 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 19 operands: 20
14	ExprTuple	21, 22
15	ExprTuple	31, 23
16	ExprTuple	31, 24
17	Literal
18	ExprTuple	36, 24
19	Literal
20	ExprTuple	31, 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 34 operand: 33
23	Operation	operator: 29 operands: 30
24	Literal
25	Literal
26	Literal
27	ExprTuple	31, 32
28	ExprTuple	33
29	Literal
30	ExprTuple	36, 33
31	Variable
32	Operation	operator: 34 operand: 36
33	Variable
34	Literal
35	ExprTuple	36
36	Variable