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, Q, V, f, j
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import VecSpaces
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Forall, Implies, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(j, Conditional(Forall(instance_param_or_params = [K, f, Q], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Implies(Forall(instance_param_or_params = [b_1_to_j], instance_expr = InSet(f__b_1_to_j, V), condition = Q__b_1_to_j), InSet(vec_summation_b1toj_fQ, V)).with_wrapping_at(2), domain = VecSpaces(K))), InSet(j, NaturalPos))))

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(j \mapsto \left\{\forall_{K, f, Q}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \in V\right)\right] \Rightarrow  \\ \left(\left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right] \in V\right) \end{array} \end{array}\right)\right] \textrm{ if } j \in \mathbb{N}^+\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: 50 body: 3
2	ExprTuple	50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 25 operand: 8
5	Operation	operator: 38 operands: 7
6	ExprTuple	8
7	ExprTuple	50, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	32, 44, 45
11	Operation	operator: 25 operand: 13
12	ExprTuple	13
13	Lambda	parameter: 41 body: 15
14	ExprTuple	41
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	41, 24
22	Operation	operator: 25 operand: 30
23	Operation	operator: 38 operands: 27
24	Operation	operator: 28 operand: 32
25	Literal
26	ExprTuple	30
27	ExprTuple	31, 41
28	Literal
29	ExprTuple	32
30	Lambda	parameters: 46 body: 33
31	Operation	operator: 34 operand: 37
32	Variable
33	Conditional	value: 36 condition: 43
34	Literal
35	ExprTuple	37
36	Operation	operator: 38 operands: 39
37	Lambda	parameters: 46 body: 40
38	Literal
39	ExprTuple	42, 41
40	Conditional	value: 42 condition: 43
41	Variable
42	Operation	operator: 44 operands: 46
43	Operation	operator: 45 operands: 46
44	Variable
45	Variable
46	ExprTuple	47
47	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
48	Lambda	parameter: 54 body: 51
49	Literal
50	Variable
51	IndexedVar	variable: 52 index: 54
52	Variable
53	ExprTuple	54
54	Variable