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 Card, Equals, Forall, InSet, SetOfAll
from proveit.numbers import 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], instance_expr = Equals(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, 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 \in \mathbb{Z}~|~|\{a~\ldotp \ldotp~b\}| \geq N}~\left(\left\{x ~\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: 43 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	47, 7
6	Lambda	parameters: 52 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19
15	Operation	operator: 20 operand: 27
16	Operation	operator: 51 operands: 22
17	Operation	operator: 43 operands: 23
18	Operation	operator: 43 operands: 24
19	Operation	operator: 25 operands: 26
20	Literal
21	ExprTuple	27
22	ExprTuple	28, 29
23	ExprTuple	53, 30
24	ExprTuple	54, 30
25	Literal
26	ExprTuple	47, 31
27	Lambda	parameter: 48 body: 33
28	Literal
29	Operation	operator: 34 operands: 35
30	Literal
31	Operation	operator: 36 operand: 49
32	ExprTuple	48
33	Conditional	value: 38 condition: 39
34	Literal
35	ExprTuple	47, 40
36	Literal
37	ExprTuple	49
38	Operation	operator: 41 operands: 42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 45 operand: 50
41	Literal
42	ExprTuple	48, 47
43	Literal
44	ExprTuple	48, 49
45	Literal
46	ExprTuple	50
47	Variable
48	Variable
49	Operation	operator: 51 operands: 52
50	Literal
51	Literal
52	ExprTuple	53, 54
53	Variable
54	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶