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, m, n
from proveit.core_expr_types import a_1_to_m
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos
from proveit.numbers.exponentiation import prod_ai_raise_n__1_to_m

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_m], instance_expr = Equals(Exp(Mult(a_1_to_m), n), prod_ai_raise_n__1_to_m), domain = Complex), And(InSet(m, NaturalPos), 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\{\forall_{a_{1}, a_{2}, \ldots, a_{m} \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{m}\right)^{n} = \left(\left(a_{1}\right)^{n} \cdot  \left(a_{2}\right)^{n} \cdot  \ldots \cdot  \left(a_{m}\right)^{n}\right)\right) \textrm{ if } m \in \mathbb{N}^+ ,  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 operand: 6
2	Operation	operator: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 29 body: 9
7	Operation	operator: 31 operands: 10
8	Operation	operator: 31 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	38, 14
11	ExprTuple	42, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 39 operands: 22
20	Operation	operator: 28 operands: 23
21	ExprRange	lambda_map: 24 start_index: 37 end_index: 38
22	ExprTuple	25, 42
23	ExprTuple	26
24	Lambda	parameter: 45 body: 27
25	Operation	operator: 28 operands: 29
26	ExprRange	lambda_map: 30 start_index: 37 end_index: 38
27	Operation	operator: 31 operands: 32
28	Literal
29	ExprTuple	33
30	Lambda	parameter: 45 body: 34
31	Literal
32	ExprTuple	41, 35
33	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
34	Operation	operator: 39 operands: 40
35	Literal
36	Lambda	parameter: 45 body: 41
37	Literal
38	Variable
39	Literal
40	ExprTuple	41, 42
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶