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

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = Conditional(Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(c, x), N), domain = sub_expr1)), N), 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(c + x\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = N \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, 35
5	Literal
6	ExprTuple	8, 9, 10, 11
7	Operation	operator: 23 operand: 18
8	Operation	operator: 32 operands: 13
9	Operation	operator: 32 operands: 14
10	Operation	operator: 32 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18
13	ExprTuple	43, 19
14	ExprTuple	44, 19
15	ExprTuple	41, 19
16	Literal
17	ExprTuple	35, 20
18	Operation	operator: 21 operand: 25
19	Literal
20	Operation	operator: 23 operand: 36
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	36
25	Lambda	parameter: 42 body: 27
26	ExprTuple	42
27	Conditional	value: 28 condition: 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	42, 36
34	Operation	operator: 37 operands: 38
35	Variable
36	Operation	operator: 39 operands: 40
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43, 44
41	Variable
42	Variable
43	Variable
44	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶