Expression of type Conditional

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, a, b, c
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, Neg, Real, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(Exp(a, Neg(b)), Neg(c)), Exp(a, Mult(b, c))), And(InSet(a, Complex), InSet(b, Real), InSet(c, Real), 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})^{-c} = a^{b \cdot c} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{R} ,  c \in \mathbb{R} ,  a \neq 0\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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