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 Conditional, Lambda, V, i, j, k, v
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, one, subtract

# build up the expression from sub-expressions
expr = Lambda(v, Conditional(Equals(VecSum(index_or_indices = [i], summand = v, domain = Interval(j, k)), ScalarMult(Add(subtract(k, j), one), v)), InSet(v, V)))

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\{\left(\sum_{i=j}^{k} v\right) = \left(\left(\left(k - j\right) + 1\right) \cdot v\right) \textrm{ if } v \in V\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 20 body: 2
1	ExprTuple	20
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 24 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	20, 10
8	Operation	operator: 11 operand: 15
9	Operation	operator: 13 operands: 14
10	Variable
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	16, 20
15	Lambda	parameter: 28 body: 18
16	Operation	operator: 26 operands: 19
17	ExprTuple	28
18	Conditional	value: 20 condition: 21
19	ExprTuple	22, 23
20	Variable
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	35, 30
28	Variable
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operand: 36
31	Literal
32	ExprTuple	36, 35
33	Literal
34	ExprTuple	36
35	Variable
36	Variable