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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [j, k], instance_expr = 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)), domain = Integer, condition = 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(K \mapsto \left[\forall_{j, k \in \mathbb{Z}~|~j \leq k}~\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]\right]\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: 35 body: 2
2	Operation	operator: 23 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 63 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 23 operand: 11
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13, 14
11	Lambda	parameter: 41 body: 16
12	Operation	operator: 55 operands: 17
13	Operation	operator: 55 operands: 18
14	Operation	operator: 19 operands: 63
15	ExprTuple	41
16	Conditional	value: 20 condition: 21
17	ExprTuple	67, 22
18	ExprTuple	66, 22
19	Literal
20	Operation	operator: 23 operand: 27
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	27
25	Literal
26	ExprTuple	41, 28
27	Lambda	parameter: 51 body: 30
28	Operation	operator: 31 operand: 35
29	ExprTuple	51
30	Conditional	value: 33 condition: 34
31	Literal
32	ExprTuple	35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 55 operands: 38
35	Variable
36	Literal
37	ExprTuple	39, 40
38	ExprTuple	51, 41
39	Operation	operator: 42 operand: 46
40	Operation	operator: 44 operands: 45
41	Variable
42	Literal
43	ExprTuple	46
44	Literal
45	ExprTuple	47, 51
46	Lambda	parameter: 59 body: 49
47	Operation	operator: 57 operands: 50
48	ExprTuple	59
49	Conditional	value: 51 condition: 52
50	ExprTuple	53, 54
51	Variable
52	Operation	operator: 55 operands: 56
53	Operation	operator: 57 operands: 58
54	Literal
55	Literal
56	ExprTuple	59, 60
57	Literal
58	ExprTuple	66, 61
59	Variable
60	Operation	operator: 62 operands: 63
61	Operation	operator: 64 operand: 67
62	Literal
63	ExprTuple	67, 66
64	Literal
65	ExprTuple	67
66	Variable
67	Variable