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
from proveit.core_expr_types import k_1_to_m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Complex, Exp, NaturalPos
from proveit.numbers.exponentiation import prod_a_raise_ki__1_to_m

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, k_1_to_m], instance_expr = Equals(prod_a_raise_ki__1_to_m, Exp(a, Add(k_1_to_m))), domains = [Complex, NaturalPos]), InSet(m, 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 \in \mathbb{C},\left(k_{1} \in \mathbb{N}^+\right), \left(k_{2} \in \mathbb{N}^+\right), \ldots, \left(k_{m} \in \mathbb{N}^+\right)}~\left(\left(a^{k_{1}} \cdot  a^{k_{2}} \cdot  \ldots \cdot  a^{k_{m}}\right) = a^{k_{1} +  k_{2} +  \ldots +  k_{m}}\right) \textrm{ if } m \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: 31 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	40, 35
6	Lambda	parameters: 7 body: 8
7	ExprTuple	41, 34
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
15	Operation	operator: 19 operands: 20
16	Operation	operator: 36 operands: 21
17	Operation	operator: 31 operands: 22
18	ExprRange	lambda_map: 23 start_index: 39 end_index: 40
19	Literal
20	ExprTuple	24
21	ExprTuple	41, 25
22	ExprTuple	41, 26
23	Lambda	parameter: 45 body: 27
24	ExprRange	lambda_map: 28 start_index: 39 end_index: 40
25	Operation	operator: 29 operands: 30
26	Literal
27	Operation	operator: 31 operands: 32
28	Lambda	parameter: 45 body: 33
29	Literal
30	ExprTuple	34
31	Literal
32	ExprTuple	42, 35
33	Operation	operator: 36 operands: 37
34	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
35	Literal
36	Literal
37	ExprTuple	41, 42
38	Lambda	parameter: 45 body: 42
39	Literal
40	Variable
41	Variable
42	IndexedVar	variable: 43 index: 45
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 ¶