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, n, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Exp, Interval, Natural, Sum, frac, one, subtract, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(zero, n)), frac(subtract(one, Exp(x, Add(n, one))), subtract(one, x))), domain = Natural)

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_{n \in \mathbb{N}}~\left(\left(\sum_{i = 0}^{n} x^{i}\right) = \frac{1 - x^{n + 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	parameter: 47 body: 5
4	ExprTuple	47
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 30 operands: 10
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	47, 13
11	Operation	operator: 14 operand: 18
12	Operation	operator: 16 operands: 17
13	Literal
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	19, 20
18	Lambda	parameter: 35 body: 22
19	Operation	operator: 45 operands: 23
20	Operation	operator: 45 operands: 24
21	ExprTuple	35
22	Conditional	value: 25 condition: 26
23	ExprTuple	48, 27
24	ExprTuple	48, 28
25	Operation	operator: 40 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 33 operand: 37
28	Operation	operator: 33 operand: 43
29	ExprTuple	43, 35
30	Literal
31	ExprTuple	35, 36
32	ExprTuple	37
33	Literal
34	ExprTuple	43
35	Variable
36	Operation	operator: 38 operands: 39
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	42, 47
40	Literal
41	ExprTuple	43, 44
42	Literal
43	Variable
44	Operation	operator: 45 operands: 46
45	Literal
46	ExprTuple	47, 48
47	Variable
48	Literal