Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶

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, L, b, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Mod, ModAbs, Natural, Real, RealPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = Forall(instance_param_or_params = [L], instance_expr = Equals(ModAbs(Add(a_1_to_i, Mod(b, L), c_1_to_j), L), ModAbs(Add(a_1_to_i, b, c_1_to_j), L)).with_wrapping_at(2), domain = RealPos), domain = Real), And(InSet(i, Natural), InSet(j, Natural)))

# 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_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{R}}~\left[\forall_{L \in \mathbb{R}^+}~\left(\begin{array}{c} \begin{array}{l} \left|a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b ~\textup{mod}~ L\right)+ c_{1} +  c_{2} +  \ldots +  c_{j}\right|_{\textup{mod}\thinspace L} =  \\ \left|a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right|_{\textup{mod}\thinspace L} \end{array} \end{array}\right)\right] \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\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: 14 operand: 5
2	Operation	operator: 16 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Lambda	parameters: 48 body: 8
6	Operation	operator: 35 operands: 9
7	Operation	operator: 35 operands: 10
8	Conditional	value: 11 condition: 12
9	ExprTuple	55, 13
10	ExprTuple	58, 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, 21
18	Lambda	parameter: 60 body: 23
19	ExprRange	lambda_map: 24 start_index: 57 end_index: 55
20	Operation	operator: 35 operands: 25
21	ExprRange	lambda_map: 26 start_index: 57 end_index: 58
22	ExprTuple	60
23	Conditional	value: 27 condition: 28
24	Lambda	parameter: 66 body: 29
25	ExprTuple	59, 40
26	Lambda	parameter: 66 body: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 35 operands: 33
29	Operation	operator: 35 operands: 34
30	Operation	operator: 35 operands: 36
31	Literal
32	ExprTuple	37, 38
33	ExprTuple	60, 39
34	ExprTuple	61, 40
35	Literal
36	ExprTuple	62, 40
37	Operation	operator: 42 operands: 41
38	Operation	operator: 42 operands: 43
39	Literal
40	Literal
41	ExprTuple	44, 60
42	Literal
43	ExprTuple	45, 60
44	Operation	operator: 47 operands: 46
45	Operation	operator: 47 operands: 48
46	ExprTuple	50, 49, 51
47	Literal
48	ExprTuple	50, 59, 51
49	Operation	operator: 52 operands: 53
50	ExprRange	lambda_map: 54 start_index: 57 end_index: 55
51	ExprRange	lambda_map: 56 start_index: 57 end_index: 58
52	Literal
53	ExprTuple	59, 60
54	Lambda	parameter: 66 body: 61
55	Variable
56	Lambda	parameter: 66 body: 62
57	Literal
58	Variable
59	Variable
60	Variable
61	IndexedVar	variable: 63 index: 66
62	IndexedVar	variable: 64 index: 66
63	Variable
64	Variable
65	ExprTuple	66
66	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶