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, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import ComplexNonZero, Exp, NaturalPos, Neg, frac

# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(frac(a, b), Neg(n)), frac(Exp(b, n), Exp(a, n))), And(InSet(a, ComplexNonZero), InSet(b, ComplexNonZero), InSet(n, NaturalPos)))

# 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\{\left(\frac{a}{b}\right)^{-n} = \frac{b^{n}}{a^{n}} \textrm{ if } a \in \mathbb{C}^{\neq 0} ,  b \in \mathbb{C}^{\neq 0} ,  n \in \mathbb{N}^+\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
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
7	Operation	operator: 29 operands: 12
8	Operation	operator: 24 operands: 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18, 19
13	ExprTuple	20, 21
14	ExprTuple	32, 22
15	ExprTuple	31, 22
16	Literal
17	ExprTuple	33, 23
18	Operation	operator: 24 operands: 25
19	Operation	operator: 26 operand: 33
20	Operation	operator: 29 operands: 28
21	Operation	operator: 29 operands: 30
22	Literal
23	Literal
24	Literal
25	ExprTuple	32, 31
26	Literal
27	ExprTuple	33
28	ExprTuple	31, 33
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Variable
33	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶