Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶

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, fi, i, j, k, x
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Integer, Interval, Mult, Sum

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(j, k)
expr = Conditional(Forall(instance_param_or_params = [j, k], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(x, fi), domain = sub_expr2), Mult(x, Sum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2))), domain = Integer), InSet(x, Complex))

# 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_{j, k \in \mathbb{Z}}~\left(\left(\sum_{i = j}^{k} \left(x \cdot f\left(i\right)\right)\right) = \left(x \cdot \left(\sum_{i = j}^{k} f\left(i\right)\right)\right)\right) \textrm{ if } x \in \mathbb{C}\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: 39 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	34, 7
6	Lambda	parameters: 44 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
15	Operation	operator: 27 operand: 23
16	Operation	operator: 31 operands: 20
17	Operation	operator: 39 operands: 21
18	Operation	operator: 39 operands: 22
19	ExprTuple	23
20	ExprTuple	34, 24
21	ExprTuple	45, 25
22	ExprTuple	46, 25
23	Lambda	parameter: 41 body: 26
24	Operation	operator: 27 operand: 30
25	Literal
26	Conditional	value: 29 condition: 36
27	Literal
28	ExprTuple	30
29	Operation	operator: 31 operands: 32
30	Lambda	parameter: 41 body: 33
31	Literal
32	ExprTuple	34, 35
33	Conditional	value: 35 condition: 36
34	Variable
35	Operation	operator: 37 operand: 41
36	Operation	operator: 39 operands: 40
37	Variable
38	ExprTuple	41
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶