Expression of type Lambda ¶

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, Lambda, 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 = Lambda([a, b, c], 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(a, b, c\right) \mapsto \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	Lambda	parameters: 1 body: 2
1	ExprTuple	51, 52, 53
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 15 operand: 20
10	Operation	operator: 15 operand: 21
11	Operation	operator: 33 operands: 17
12	Operation	operator: 33 operands: 18
13	Operation	operator: 33 operands: 19
14	ExprTuple	20
15	Literal
16	ExprTuple	21
17	ExprTuple	51, 22
18	ExprTuple	52, 22
19	ExprTuple	53, 22
20	Lambda	parameter: 42 body: 23
21	Lambda	parameter: 42 body: 24
22	Literal
23	Conditional	value: 25 condition: 26
24	Conditional	value: 27 condition: 28
25	Operation	operator: 31 operand: 42
26	Operation	operator: 33 operands: 30
27	Operation	operator: 31 operand: 36
28	Operation	operator: 33 operands: 34
29	ExprTuple	42
30	ExprTuple	42, 35
31	Variable
32	ExprTuple	36
33	Literal
34	ExprTuple	42, 37
35	Operation	operator: 40 operands: 38
36	Operation	operator: 49 operands: 39
37	Operation	operator: 40 operands: 41
38	ExprTuple	51, 52
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	44, 45
42	Variable
43	Operation	operator: 46 operand: 53
44	Operation	operator: 49 operands: 48
45	Operation	operator: 49 operands: 50
46	Literal
47	ExprTuple	53
48	ExprTuple	51, 53
49	Literal
50	ExprTuple	52, 53
51	Variable
52	Variable
53	Variable

Expression of type Lambda¶

from the theory of proveit.numbers.summation¶

Expression of type Lambda ¶

from the theory of proveit.numbers.summation ¶