Expression of type Conditional ¶

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

# build up the expression from sub-expressions
expr = Conditional(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)), And(InSet(x, Complex), NotEquals(x, one)))

# 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())

\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) \textrm{ if } x \in \mathbb{C} ,  x \neq 1\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶