Expression of type And

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 And, Equals, Forall, TRUE
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 = And(TRUE, 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())

\top \land \left[\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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 12 operands: 1
1	ExprTuple	2, 3
2	Literal
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 74 body: 8
7	ExprTuple	74
8	Conditional	value: 9 condition: 10
9	Operation	operator: 21 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 30 operand: 23
15	Operation	operator: 32 operands: 19
16	Operation	operator: 54 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	23
19	ExprTuple	24, 38
20	ExprTuple	74, 25
21	Literal
22	ExprTuple	26, 27
23	Lambda	parameter: 60 body: 28
24	Operation	operator: 72 operands: 29
25	Literal
26	Operation	operator: 30 operand: 36
27	Operation	operator: 32 operands: 33
28	Conditional	value: 47 condition: 34
29	ExprTuple	75, 35
30	Literal
31	ExprTuple	36
32	Literal
33	ExprTuple	37, 38
34	Operation	operator: 54 operands: 39
35	Operation	operator: 57 operand: 46
36	Lambda	parameter: 60 body: 42
37	Operation	operator: 72 operands: 43
38	Operation	operator: 72 operands: 44
39	ExprTuple	60, 45
40	ExprTuple	46
41	ExprTuple	60
42	Conditional	value: 47 condition: 48
43	ExprTuple	75, 49
44	ExprTuple	75, 50
45	Operation	operator: 64 operands: 51
46	Operation	operator: 66 operands: 52
47	Operation	operator: 66 operands: 53
48	Operation	operator: 54 operands: 55
49	Operation	operator: 57 operand: 62
50	Operation	operator: 57 operand: 70
51	ExprTuple	69, 71
52	ExprTuple	70, 59
53	ExprTuple	70, 60
54	Literal
55	ExprTuple	60, 61
56	ExprTuple	62
57	Literal
58	ExprTuple	70
59	Operation	operator: 72 operands: 63
60	Variable
61	Operation	operator: 64 operands: 65
62	Operation	operator: 66 operands: 67
63	ExprTuple	74, 68
64	Literal
65	ExprTuple	69, 74
66	Literal
67	ExprTuple	70, 71
68	Literal
69	Literal
70	Variable
71	Operation	operator: 72 operands: 73
72	Literal
73	ExprTuple	74, 75
74	Variable
75	Literal