Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 49 body: 2
1	ExprTuple	49
2	Conditional	value: 3 condition: 4
3	Operation	operator: 24 operand: 7
4	Operation	operator: 37 operands: 6
5	ExprTuple	7
6	ExprTuple	49, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	31, 43, 44
10	Operation	operator: 24 operand: 12
11	ExprTuple	12
12	Lambda	parameter: 40 body: 14
13	ExprTuple	40
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	40, 23
21	Operation	operator: 24 operand: 29
22	Operation	operator: 37 operands: 26
23	Operation	operator: 27 operand: 31
24	Literal
25	ExprTuple	29
26	ExprTuple	30, 40
27	Literal
28	ExprTuple	31
29	Lambda	parameters: 45 body: 32
30	Operation	operator: 33 operand: 36
31	Variable
32	Conditional	value: 35 condition: 42
33	Literal
34	ExprTuple	36
35	Operation	operator: 37 operands: 38
36	Lambda	parameters: 45 body: 39
37	Literal
38	ExprTuple	41, 40
39	Conditional	value: 41 condition: 42
40	Variable
41	Operation	operator: 43 operands: 45
42	Operation	operator: 44 operands: 45
43	Variable
44	Variable
45	ExprTuple	46
46	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
47	Lambda	parameter: 53 body: 50
48	Literal
49	Variable
50	IndexedVar	variable: 51 index: 53
51	Variable
52	ExprTuple	53
53	Variable