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, N, a, b, c, x
from proveit.logic import Card, Equals, Forall, InSet, SetOfAll
from proveit.numbers import Add, Integer, Interval, Mod, NaturalPos, greater_eq, one, subtract, zero

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = Conditional(Forall(instance_param_or_params = [a, b, c], instance_expr = Equals(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(x, c), N), domain = sub_expr1), Interval(zero, subtract(N, one))), domain = Integer, condition = greater_eq(Card(sub_expr1), N)), InSet(N, NaturalPos))

# 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, b, c \in \mathbb{Z}~|~|\{a~\ldotp \ldotp~b\}| \geq N}~\left(\left\{\left(x + c\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}} = \{0~\ldotp \ldotp~N - 1\}\right) \textrm{ if } N \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: 3 operand: 6
2	Operation	operator: 45 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	50, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	59, 60, 58
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19, 20, 21
16	Operation	operator: 22 operand: 30
17	Operation	operator: 55 operands: 24
18	Operation	operator: 45 operands: 25
19	Operation	operator: 45 operands: 26
20	Operation	operator: 45 operands: 27
21	Operation	operator: 28 operands: 29
22	Literal
23	ExprTuple	30
24	ExprTuple	31, 32
25	ExprTuple	59, 33
26	ExprTuple	60, 33
27	ExprTuple	58, 33
28	Literal
29	ExprTuple	50, 34
30	Lambda	parameter: 57 body: 36
31	Literal
32	Operation	operator: 53 operands: 37
33	Literal
34	Operation	operator: 38 operand: 51
35	ExprTuple	57
36	Conditional	value: 40 condition: 41
37	ExprTuple	50, 42
38	Literal
39	ExprTuple	51
40	Operation	operator: 43 operands: 44
41	Operation	operator: 45 operands: 46
42	Operation	operator: 47 operand: 52
43	Literal
44	ExprTuple	49, 50
45	Literal
46	ExprTuple	57, 51
47	Literal
48	ExprTuple	52
49	Operation	operator: 53 operands: 54
50	Variable
51	Operation	operator: 55 operands: 56
52	Literal
53	Literal
54	ExprTuple	57, 58
55	Literal
56	ExprTuple	59, 60
57	Variable
58	Variable
59	Variable
60	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶