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 Lambda, a, b, i, v, va, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, Less, one

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = Lambda(v, Forall(instance_param_or_params = [a, b], instance_expr = Equals(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, b)), VecAdd(va, VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(Add(a, one), b)))), domain = Integer, condition = Less(a, b)))

expr:

# 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 \in \mathbb{Z}~|~a < b}~\left(\left(\sum_{i=a}^{b} v\left(i\right)\right) = \left(v\left(a\right) + \left(\sum_{i=a + 1}^{b} v\left(i\right)\right)\right)\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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