Expression of type Lambda ¶

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, Lambda, 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 = Lambda(N, 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())

N \mapsto \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	Lambda	parameter: 52 body: 2
1	ExprTuple	52
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 47 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	52, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	61, 62, 60
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22, 23
18	Operation	operator: 24 operand: 32
19	Operation	operator: 57 operands: 26
20	Operation	operator: 47 operands: 27
21	Operation	operator: 47 operands: 28
22	Operation	operator: 47 operands: 29
23	Operation	operator: 30 operands: 31
24	Literal
25	ExprTuple	32
26	ExprTuple	33, 34
27	ExprTuple	61, 35
28	ExprTuple	62, 35
29	ExprTuple	60, 35
30	Literal
31	ExprTuple	52, 36
32	Lambda	parameter: 59 body: 38
33	Literal
34	Operation	operator: 55 operands: 39
35	Literal
36	Operation	operator: 40 operand: 53
37	ExprTuple	59
38	Conditional	value: 42 condition: 43
39	ExprTuple	52, 44
40	Literal
41	ExprTuple	53
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 49 operand: 54
45	Literal
46	ExprTuple	51, 52
47	Literal
48	ExprTuple	59, 53
49	Literal
50	ExprTuple	54
51	Operation	operator: 55 operands: 56
52	Variable
53	Operation	operator: 57 operands: 58
54	Literal
55	Literal
56	ExprTuple	59, 60
57	Literal
58	ExprTuple	61, 62
59	Variable
60	Variable
61	Variable
62	Variable

Expression of type Lambda¶

from the theory of proveit.numbers.modular¶

Expression of type Lambda ¶

from the theory of proveit.numbers.modular ¶