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, ExprRange, IndexedVar, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Mult, NaturalPos, one, sqrt

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Equals(sqrt(Mult(a_1_to_n)), Mult(ExprRange(sub_expr1, sqrt(IndexedVar(a, sub_expr1)), one, n))), domain = Complex), 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_{n} \in \mathbb{C}}~\left(\sqrt{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right)} = \left(\sqrt{\left(a_{1}\right)} \cdot  \sqrt{\left(a_{2}\right)} \cdot  \ldots \cdot  \sqrt{\left(a_{n}\right)}\right)\right) \textrm{ if } 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: 27 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	33, 7
6	Lambda	parameters: 25 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
15	Operation	operator: 34 operands: 18
16	Operation	operator: 24 operands: 19
17	ExprRange	lambda_map: 20 start_index: 43 end_index: 33
18	ExprTuple	21, 37
19	ExprTuple	22
20	Lambda	parameter: 42 body: 23
21	Operation	operator: 24 operands: 25
22	ExprRange	lambda_map: 26 start_index: 43 end_index: 33
23	Operation	operator: 27 operands: 28
24	Literal
25	ExprTuple	29
26	Lambda	parameter: 42 body: 30
27	Literal
28	ExprTuple	36, 31
29	ExprRange	lambda_map: 32 start_index: 43 end_index: 33
30	Operation	operator: 34 operands: 35
31	Literal
32	Lambda	parameter: 42 body: 36
33	Variable
34	Literal
35	ExprTuple	36, 37
36	IndexedVar	variable: 38 index: 42
37	Operation	operator: 40 operands: 41
38	Variable
39	ExprTuple	42
40	Literal
41	ExprTuple	43, 44
42	Variable
43	Literal
44	Literal

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶