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 Equals, Forall, InSet, NotEquals
from proveit.numbers import Complex, Exp, Integer, Mult, Neg, zero

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Exp(Exp(a, b), Neg(n)), Exp(a, Neg(Mult(b, n)))), domain = Complex, condition = NotEquals(a, zero)), InSet(n, Integer))

# 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\{\forall_{a, b \in \mathbb{C}~|~a \neq 0}~\left((a^{b})^{-n} = a^{-\left(b \cdot n\right)}\right) \textrm{ if } n \in \mathbb{Z}\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 operand: 6
2	Operation	operator: 23 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	42, 7
6	Lambda	parameters: 33 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19
15	Operation	operator: 32 operands: 20
16	Operation	operator: 32 operands: 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 25 operands: 26
20	ExprTuple	27, 28
21	ExprTuple	37, 29
22	ExprTuple	37, 30
23	Literal
24	ExprTuple	41, 30
25	Literal
26	ExprTuple	37, 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 35 operand: 42
29	Operation	operator: 35 operand: 38
30	Literal
31	Literal
32	Literal
33	ExprTuple	37, 41
34	ExprTuple	42
35	Literal
36	ExprTuple	38
37	Variable
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶