Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 21 body: 3
2	ExprTuple	21
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 25 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	21, 11
9	Operation	operator: 12 operand: 16
10	Operation	operator: 14 operands: 15
11	Variable
12	Literal
13	ExprTuple	16
14	Literal
15	ExprTuple	17, 21
16	Lambda	parameter: 29 body: 19
17	Operation	operator: 27 operands: 20
18	ExprTuple	29
19	Conditional	value: 21 condition: 22
20	ExprTuple	23, 24
21	Variable
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	36, 31
29	Variable
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operand: 37
32	Literal
33	ExprTuple	37, 36
34	Literal
35	ExprTuple	37
36	Variable
37	Variable