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, Neg(b)), Neg(n)), Exp(a, 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^{b \cdot n}\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: 24 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	40, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	38, 43
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19, 20
16	Operation	operator: 33 operands: 21
17	Operation	operator: 33 operands: 22
18	Operation	operator: 24 operands: 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 26 operands: 27
21	ExprTuple	28, 29
22	ExprTuple	38, 30
23	ExprTuple	38, 31
24	Literal
25	ExprTuple	43, 31
26	Literal
27	ExprTuple	38, 32
28	Operation	operator: 33 operands: 34
29	Operation	operator: 41 operand: 40
30	Operation	operator: 36 operands: 37
31	Literal
32	Literal
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	40
36	Literal
37	ExprTuple	43, 40
38	Variable
39	Operation	operator: 41 operand: 43
40	Variable
41	Literal
42	ExprTuple	43
43	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶