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 Equals, Forall, InClass
from proveit.numbers import Add, Interval, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(V, Conditional(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), InClass(V, VecSpaces(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(V \mapsto \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) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\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: 24 body: 3
2	ExprTuple	24
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	24, 11
10	Lambda	parameter: 34 body: 13
11	Operation	operator: 14 operand: 18
12	ExprTuple	34
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 38 operands: 21
18	Variable
19	Literal
20	ExprTuple	22, 23
21	ExprTuple	34, 24
22	Operation	operator: 25 operand: 29
23	Operation	operator: 27 operands: 28
24	Variable
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	30, 34
29	Lambda	parameter: 42 body: 32
30	Operation	operator: 40 operands: 33
31	ExprTuple	42
32	Conditional	value: 34 condition: 35
33	ExprTuple	36, 37
34	Variable
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	Literal
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	49, 44
42	Variable
43	Operation	operator: 45 operands: 46
44	Operation	operator: 47 operand: 50
45	Literal
46	ExprTuple	50, 49
47	Literal
48	ExprTuple	50
49	Variable
50	Variable