Expression of type Lambda ¶

from the theory of proveit.linear_algebra.addition ¶

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 Function, Lambda, a, b, c, i, v, vi
from proveit.linear_algebra import VecSum
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, subtract

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = Lambda(v, Forall(instance_param_or_params = [a, b, c], instance_expr = Equals(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, b)), VecSum(index_or_indices = sub_expr1, summand = Function(v, [subtract(i, c)]), domain = Interval(Add(a, c), Add(b, c)))), domain = 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())

v \mapsto \left[\forall_{a, b, c \in \mathbb{Z}}~\left(\left(\sum_{i=a}^{b} v\left(i\right)\right) = \left(\sum_{i=a + c}^{b + c} v\left(i - c\right)\right)\right)\right]

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameter: 36 body: 2
1	ExprTuple	36
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	56, 57, 58
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17, 18
14	Operation	operator: 20 operand: 25
15	Operation	operator: 20 operand: 26
16	Operation	operator: 38 operands: 22
17	Operation	operator: 38 operands: 23
18	Operation	operator: 38 operands: 24
19	ExprTuple	25
20	Literal
21	ExprTuple	26
22	ExprTuple	56, 27
23	ExprTuple	57, 27
24	ExprTuple	58, 27
25	Lambda	parameter: 47 body: 28
26	Lambda	parameter: 47 body: 29
27	Literal
28	Conditional	value: 30 condition: 31
29	Conditional	value: 32 condition: 33
30	Operation	operator: 36 operand: 47
31	Operation	operator: 38 operands: 35
32	Operation	operator: 36 operand: 41
33	Operation	operator: 38 operands: 39
34	ExprTuple	47
35	ExprTuple	47, 40
36	Variable
37	ExprTuple	41
38	Literal
39	ExprTuple	47, 42
40	Operation	operator: 45 operands: 43
41	Operation	operator: 54 operands: 44
42	Operation	operator: 45 operands: 46
43	ExprTuple	56, 57
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	49, 50
47	Variable
48	Operation	operator: 51 operand: 58
49	Operation	operator: 54 operands: 53
50	Operation	operator: 54 operands: 55
51	Literal
52	ExprTuple	58
53	ExprTuple	56, 58
54	Literal
55	ExprTuple	57, 58
56	Variable
57	Variable
58	Variable

Expression of type Lambda¶

from the theory of proveit.linear_algebra.addition¶

Expression of type Lambda ¶

from the theory of proveit.linear_algebra.addition ¶