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, a, alpha, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Integer, Interval, LessEq, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [k]
expr = Conditional(Forall(instance_param_or_params = [alpha], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(Add(b, one), c))))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), And(LessEq(a, b), LessEq(b, c)).with_total_ordering_style()))

# 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_{\alpha}~\left(\left(\sum_{k = a}^{c} \alpha_{k}\right) = \left(\left(\sum_{k = a}^{b} \alpha_{k}\right) + \left(\sum_{k = b + 1}^{c} \alpha_{k}\right)\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  a \leq b \leq c\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: 16 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9, 10
6	Lambda	parameter: 48 body: 12
7	Operation	operator: 50 operands: 13
8	Operation	operator: 50 operands: 14
9	Operation	operator: 50 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprTuple	48
12	Operation	operator: 18 operands: 19
13	ExprTuple	58, 20
14	ExprTuple	63, 20
15	ExprTuple	60, 20
16	Literal
17	ExprTuple	21, 22
18	Literal
19	ExprTuple	23, 24
20	Literal
21	Operation	operator: 25 operands: 55
22	Operation	operator: 25 operands: 26
23	Operation	operator: 34 operand: 29
24	Operation	operator: 61 operands: 28
25	Literal
26	ExprTuple	63, 60
27	ExprTuple	29
28	ExprTuple	30, 31
29	Lambda	parameter: 53 body: 32
30	Operation	operator: 34 operand: 37
31	Operation	operator: 34 operand: 38
32	Conditional	value: 44 condition: 36
33	ExprTuple	37
34	Literal
35	ExprTuple	38
36	Operation	operator: 50 operands: 39
37	Lambda	parameter: 53 body: 40
38	Lambda	parameter: 53 body: 41
39	ExprTuple	53, 42
40	Conditional	value: 44 condition: 43
41	Conditional	value: 44 condition: 45
42	Operation	operator: 56 operands: 46
43	Operation	operator: 50 operands: 47
44	IndexedVar	variable: 48 index: 53
45	Operation	operator: 50 operands: 51
46	ExprTuple	58, 60
47	ExprTuple	53, 52
48	Variable
49	ExprTuple	53
50	Literal
51	ExprTuple	53, 54
52	Operation	operator: 56 operands: 55
53	Variable
54	Operation	operator: 56 operands: 57
55	ExprTuple	58, 63
56	Literal
57	ExprTuple	59, 60
58	Variable
59	Operation	operator: 61 operands: 62
60	Variable
61	Literal
62	ExprTuple	63, 64
63	Variable
64	Literal

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶