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

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Exp(x, i)
sub_expr3 = Add(m, one)
sub_expr4 = subtract(one, x)
expr = Forall(instance_param_or_params = [m], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, sub_expr3)), frac(subtract(one, Exp(x, Add(m, two))), sub_expr4)), domain = Natural, condition = Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, m)), frac(subtract(one, Exp(x, sub_expr3)), sub_expr4)))

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_{m \in \mathbb{N}~|~\left(\sum_{i = 0}^{m} x^{i}\right) = \frac{1 - x^{m + 1}}{1 - x}}~\left(\left(\sum_{i = 0}^{m + 1} x^{i}\right) = \frac{1 - x^{m + 2}}{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: 71 body: 5
4	ExprTuple	71
5	Conditional	value: 6 condition: 7
6	Operation	operator: 18 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 27 operand: 20
12	Operation	operator: 29 operands: 16
13	Operation	operator: 51 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	20
16	ExprTuple	21, 35
17	ExprTuple	71, 22
18	Literal
19	ExprTuple	23, 24
20	Lambda	parameter: 57 body: 25
21	Operation	operator: 69 operands: 26
22	Literal
23	Operation	operator: 27 operand: 33
24	Operation	operator: 29 operands: 30
25	Conditional	value: 44 condition: 31
26	ExprTuple	72, 32
27	Literal
28	ExprTuple	33
29	Literal
30	ExprTuple	34, 35
31	Operation	operator: 51 operands: 36
32	Operation	operator: 54 operand: 43
33	Lambda	parameter: 57 body: 39
34	Operation	operator: 69 operands: 40
35	Operation	operator: 69 operands: 41
36	ExprTuple	57, 42
37	ExprTuple	43
38	ExprTuple	57
39	Conditional	value: 44 condition: 45
40	ExprTuple	72, 46
41	ExprTuple	72, 47
42	Operation	operator: 61 operands: 48
43	Operation	operator: 63 operands: 49
44	Operation	operator: 63 operands: 50
45	Operation	operator: 51 operands: 52
46	Operation	operator: 54 operand: 59
47	Operation	operator: 54 operand: 67
48	ExprTuple	66, 68
49	ExprTuple	67, 56
50	ExprTuple	67, 57
51	Literal
52	ExprTuple	57, 58
53	ExprTuple	59
54	Literal
55	ExprTuple	67
56	Operation	operator: 69 operands: 60
57	Variable
58	Operation	operator: 61 operands: 62
59	Operation	operator: 63 operands: 64
60	ExprTuple	71, 65
61	Literal
62	ExprTuple	66, 71
63	Literal
64	ExprTuple	67, 68
65	Literal
66	Literal
67	Variable
68	Operation	operator: 69 operands: 70
69	Literal
70	ExprTuple	71, 72
71	Variable
72	Literal