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, x
from proveit.logic import And, Card, Equals, InSet, SetOfAll
from proveit.numbers import 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(x, N), domain = sub_expr1), Interval(zero, subtract(N, one))), And(InSet(a, Integer), InSet(b, 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\{x ~\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} ,  |\{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
7	Operation	operator: 12 operand: 19
8	Operation	operator: 43 operands: 14
9	Operation	operator: 35 operands: 15
10	Operation	operator: 35 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19
14	ExprTuple	20, 21
15	ExprTuple	45, 22
16	ExprTuple	46, 22
17	Literal
18	ExprTuple	39, 23
19	Lambda	parameter: 40 body: 25
20	Literal
21	Operation	operator: 26 operands: 27
22	Literal
23	Operation	operator: 28 operand: 41
24	ExprTuple	40
25	Conditional	value: 30 condition: 31
26	Literal
27	ExprTuple	39, 32
28	Literal
29	ExprTuple	41
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operand: 42
33	Literal
34	ExprTuple	40, 39
35	Literal
36	ExprTuple	40, 41
37	Literal
38	ExprTuple	42
39	Variable
40	Variable
41	Operation	operator: 43 operands: 44
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶