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 Conditional, Lambda, c, d, fj, gj, j, x
from proveit.logic import Equals, Forall, InSet
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(x, Conditional(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), InSet(x, 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())

x \mapsto \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) \textrm{ if } x \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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