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, K, Lambda, V, i, j, k, v
from proveit.linear_algebra import ScalarMult, VecSpaces, VecSum
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Integer, Interval, LessEq, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([j, k], Conditional(Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [v], instance_expr = Equals(VecSum(index_or_indices = [i], summand = v, domain = Interval(j, k)), ScalarMult(Add(subtract(k, j), one), v)), domain = V), domain = VecSpaces(K)), And(InSet(j, Integer), InSet(k, Integer), LessEq(j, k)))))

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(\left(j, k\right) \mapsto \left\{\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{v \in V}~\left(\left(\sum_{i=j}^{k} v\right) = \left(\left(\left(k - j\right) + 1\right) \cdot v\right)\right)\right] \textrm{ if } j \in \mathbb{Z} ,  k \in \mathbb{Z} ,  j \leq k\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	parameters: 60 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 20 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10, 11
8	Lambda	parameter: 38 body: 13
9	Operation	operator: 52 operands: 14
10	Operation	operator: 52 operands: 15
11	Operation	operator: 16 operands: 60
12	ExprTuple	38
13	Conditional	value: 17 condition: 18
14	ExprTuple	64, 19
15	ExprTuple	63, 19
16	Literal
17	Operation	operator: 20 operand: 24
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24
22	Literal
23	ExprTuple	38, 25
24	Lambda	parameter: 48 body: 27
25	Operation	operator: 28 operand: 32
26	ExprTuple	48
27	Conditional	value: 30 condition: 31
28	Literal
29	ExprTuple	32
30	Operation	operator: 33 operands: 34
31	Operation	operator: 52 operands: 35
32	Variable
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	48, 38
36	Operation	operator: 39 operand: 43
37	Operation	operator: 41 operands: 42
38	Variable
39	Literal
40	ExprTuple	43
41	Literal
42	ExprTuple	44, 48
43	Lambda	parameter: 56 body: 46
44	Operation	operator: 54 operands: 47
45	ExprTuple	56
46	Conditional	value: 48 condition: 49
47	ExprTuple	50, 51
48	Variable
49	Operation	operator: 52 operands: 53
50	Operation	operator: 54 operands: 55
51	Literal
52	Literal
53	ExprTuple	56, 57
54	Literal
55	ExprTuple	63, 58
56	Variable
57	Operation	operator: 59 operands: 60
58	Operation	operator: 61 operand: 64
59	Literal
60	ExprTuple	64, 63
61	Literal
62	ExprTuple	64
63	Variable
64	Variable