Expression of type Lambda

from the theory of proveit.numbers.summation

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, c, d, f, fj, g, gj, j, x
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Integer, Interval, Mult, Sum

# build up the expression from sub-expressions
sub_expr1 = [j]
sub_expr2 = Interval(c, d)
expr = Lambda([f, g], Forall(instance_param_or_params = [x], instance_expr = Forall(instance_param_or_params = [c, d], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(Mult(x, gj), fj), domain = sub_expr2), Mult(x, Sum(index_or_indices = sub_expr1, summand = Mult(gj, fj), domain = sub_expr2))), domain = Integer), domain = Complex))

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, g\right) \mapsto \left[\forall_{x \in \mathbb{C}}~\left[\forall_{c, d \in \mathbb{Z}}~\left(\left(\sum_{j = c}^{d} \left(\left(x \cdot g\left(j\right)\right) \cdot f\left(j\right)\right)\right) = \left(x \cdot \left(\sum_{j = c}^{d} \left(g\left(j\right) \cdot f\left(j\right)\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	Lambda	parameters: 1 body: 2
1	ExprTuple	52, 51
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 47 body: 6
5	ExprTuple	47
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 45 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	47, 13
12	Lambda	parameters: 55 body: 14
13	Literal
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	23, 24
21	Operation	operator: 33 operand: 29
22	Operation	operator: 43 operands: 26
23	Operation	operator: 45 operands: 27
24	Operation	operator: 45 operands: 28
25	ExprTuple	29
26	ExprTuple	47, 30
27	ExprTuple	57, 31
28	ExprTuple	58, 31
29	Lambda	parameter: 56 body: 32
30	Operation	operator: 33 operand: 36
31	Literal
32	Conditional	value: 35 condition: 41
33	Literal
34	ExprTuple	36
35	Operation	operator: 43 operands: 37
36	Lambda	parameter: 56 body: 38
37	ExprTuple	39, 49
38	Conditional	value: 40 condition: 41
39	Operation	operator: 43 operands: 42
40	Operation	operator: 43 operands: 44
41	Operation	operator: 45 operands: 46
42	ExprTuple	47, 48
43	Literal
44	ExprTuple	48, 49
45	Literal
46	ExprTuple	56, 50
47	Variable
48	Operation	operator: 51 operand: 56
49	Operation	operator: 52 operand: 56
50	Operation	operator: 54 operands: 55
51	Variable
52	Variable
53	ExprTuple	56
54	Literal
55	ExprTuple	57, 58
56	Variable
57	Variable
58	Variable