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, Function, a, b, c, f, fx, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Interval, Sum, subtract

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = Function(f, [subtract(x, c)]), domain = Interval(Add(a, c), Add(b, c)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, 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\{\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\sum_{x = a + c}^{b + c} f\left(x - c\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 13 operand: 18
8	Operation	operator: 13 operand: 19
9	Operation	operator: 31 operands: 15
10	Operation	operator: 31 operands: 16
11	Operation	operator: 31 operands: 17
12	ExprTuple	18
13	Literal
14	ExprTuple	19
15	ExprTuple	49, 20
16	ExprTuple	50, 20
17	ExprTuple	51, 20
18	Lambda	parameter: 40 body: 21
19	Lambda	parameter: 40 body: 22
20	Literal
21	Conditional	value: 23 condition: 24
22	Conditional	value: 25 condition: 26
23	Operation	operator: 29 operand: 40
24	Operation	operator: 31 operands: 28
25	Operation	operator: 29 operand: 34
26	Operation	operator: 31 operands: 32
27	ExprTuple	40
28	ExprTuple	40, 33
29	Variable
30	ExprTuple	34
31	Literal
32	ExprTuple	40, 35
33	Operation	operator: 38 operands: 36
34	Operation	operator: 47 operands: 37
35	Operation	operator: 38 operands: 39
36	ExprTuple	49, 50
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42, 43
40	Variable
41	Operation	operator: 44 operand: 51
42	Operation	operator: 47 operands: 46
43	Operation	operator: 47 operands: 48
44	Literal
45	ExprTuple	51
46	ExprTuple	49, 51
47	Literal
48	ExprTuple	50, 51
49	Variable
50	Variable
51	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶