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 And, Card, Equals, InSet, SetOfAll
from proveit.numbers import Add, Integer, Interval, Mod, greater_eq, one, subtract, zero

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

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

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶