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
from proveit.numbers import Add, Exp, Integer, Interval, LessEq, Sum, frac, one, subtract

# build up the expression from sub-expressions
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))

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_{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)

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