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 Lambda, Q, f, j, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, NaturalPos
from proveit.numbers.summation import summation_b1toj_fQ

# build up the expression from sub-expressions
expr = Lambda([f, Q], Forall(instance_param_or_params = [n, j], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(vec_summation_b1toj_fQ, summation_b1toj_fQ), domain = Complex), domain = 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(f, Q\right) \mapsto \left[\forall_{n, j \in \mathbb{N}^+}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in \mathbb{C}}~\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] = \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]\right)\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	45, 46
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	35, 52
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 26 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 14
12	Lambda	parameters: 15 body: 16
13	Operation	operator: 39 operands: 17
14	Operation	operator: 39 operands: 18
15	ExprTuple	19
16	Conditional	value: 20 condition: 21
17	ExprTuple	35, 22
18	ExprTuple	52, 22
19	ExprRange	lambda_map: 23 start_index: 51 end_index: 35
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Lambda	parameter: 56 body: 43
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30
28	Operation	operator: 31 operand: 36
29	Operation	operator: 32 operand: 36
30	ExprRange	lambda_map: 34 start_index: 51 end_index: 35
31	Literal
32	Literal
33	ExprTuple	36
34	Lambda	parameter: 56 body: 37
35	Variable
36	Lambda	parameters: 47 body: 38
37	Operation	operator: 39 operands: 40
38	Conditional	value: 41 condition: 42
39	Literal
40	ExprTuple	43, 44
41	Operation	operator: 45 operands: 47
42	Operation	operator: 46 operands: 47
43	IndexedVar	variable: 48 index: 56
44	Literal
45	Variable
46	Variable
47	ExprTuple	49
48	Variable
49	ExprRange	lambda_map: 50 start_index: 51 end_index: 52
50	Lambda	parameter: 56 body: 53
51	Literal
52	Variable
53	IndexedVar	variable: 54 index: 56
54	Variable
55	ExprTuple	56
56	Variable