Expression of type Forall

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 i, j, k, x
from proveit.logic import Equals, Forall, NotEquals
from proveit.numbers import Add, Complex, Exp, Integer, Interval, LessEq, Sum, frac, one, subtract

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x], instance_expr = Forall(instance_param_or_params = [j, k], instance_expr = Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(j, k)), frac(subtract(Exp(x, j), Exp(x, Add(k, one))), subtract(one, x))), domain = Integer, condition = LessEq(j, k)), domain = Complex, condition = NotEquals(x, one))

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())

\forall_{x \in \mathbb{C}~|~x \neq 1}~\left[\forall_{j, k \in \mathbb{Z}~|~j \leq k}~\left(\left(\sum_{i = j}^{k} x^{i}\right) = \frac{x^{j} - x^{k + 1}}{1 - x}\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 63 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 59 body: 12
10	Operation	operator: 49 operands: 13
11	Operation	operator: 14 operands: 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	63, 18
14	Literal
15	ExprTuple	63, 68
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27
23	Operation	operator: 28 operand: 35
24	Operation	operator: 30 operands: 31
25	Operation	operator: 49 operands: 32
26	Operation	operator: 49 operands: 33
27	Operation	operator: 34 operands: 59
28	Literal
29	ExprTuple	35
30	Literal
31	ExprTuple	36, 37
32	ExprTuple	62, 38
33	ExprTuple	67, 38
34	Literal
35	Lambda	parameter: 55 body: 40
36	Operation	operator: 65 operands: 41
37	Operation	operator: 65 operands: 42
38	Literal
39	ExprTuple	55
40	Conditional	value: 43 condition: 44
41	ExprTuple	45, 46
42	ExprTuple	68, 47
43	Operation	operator: 60 operands: 48
44	Operation	operator: 49 operands: 50
45	Operation	operator: 60 operands: 51
46	Operation	operator: 53 operand: 57
47	Operation	operator: 53 operand: 63
48	ExprTuple	63, 55
49	Literal
50	ExprTuple	55, 56
51	ExprTuple	63, 62
52	ExprTuple	57
53	Literal
54	ExprTuple	63
55	Variable
56	Operation	operator: 58 operands: 59
57	Operation	operator: 60 operands: 61
58	Literal
59	ExprTuple	62, 67
60	Literal
61	ExprTuple	63, 64
62	Variable
63	Variable
64	Operation	operator: 65 operands: 66
65	Literal
66	ExprTuple	67, 68
67	Variable
68	Literal