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, m, n
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, NaturalPos, frac, subtract, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(frac(Exp(a, m), Exp(a, n)), Exp(a, subtract(m, n))), And(InSet(a, Complex), InSet(m, NaturalPos), InSet(n, NaturalPos), 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\{\frac{a^{m}}{a^{n}} = a^{m - n} \textrm{ if } a \in \mathbb{C} ,  m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+ ,  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: 13 operands: 14
8	Operation	operator: 29 operands: 15
9	Operation	operator: 18 operands: 16
10	Operation	operator: 18 operands: 17
11	Operation	operator: 18 operands: 19
12	Operation	operator: 20 operands: 21
13	Literal
14	ExprTuple	22, 23
15	ExprTuple	33, 24
16	ExprTuple	33, 25
17	ExprTuple	34, 26
18	Literal
19	ExprTuple	38, 26
20	Literal
21	ExprTuple	33, 27
22	Operation	operator: 29 operands: 28
23	Operation	operator: 29 operands: 30
24	Operation	operator: 31 operands: 32
25	Literal
26	Literal
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	33, 38
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Variable
35	Operation	operator: 36 operand: 38
36	Literal
37	ExprTuple	38
38	Variable