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, Lambda, N, a, b, c, x
from proveit.logic import Bijections, Forall, InSet
from proveit.numbers import Add, Integer, Interval, Mod, NaturalPos, one, subtract, zero

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, b, c], instance_expr = InSet(Lambda(x, Mod(Add(x, c), N)), Bijections(Interval(a, b), Interval(zero, subtract(N, one)))), domain = Integer), 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, c \in \mathbb{Z}}~\left(\left[x \mapsto \left(\left(x + c\right) ~\textup{mod}~ N\right)\right] \in \left[\{a~\ldotp \ldotp~b\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~N - 1\}\right]\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: 26 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	46, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	38, 39, 43
9	Conditional	value: 10 condition: 11
10	Operation	operator: 26 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19
15	Lambda	parameter: 42 body: 21
16	Operation	operator: 22 operands: 23
17	Operation	operator: 26 operands: 24
18	Operation	operator: 26 operands: 25
19	Operation	operator: 26 operands: 27
20	ExprTuple	42
21	Operation	operator: 28 operands: 29
22	Literal
23	ExprTuple	30, 31
24	ExprTuple	38, 32
25	ExprTuple	39, 32
26	Literal
27	ExprTuple	43, 32
28	Literal
29	ExprTuple	33, 46
30	Operation	operator: 35 operands: 34
31	Operation	operator: 35 operands: 36
32	Literal
33	Operation	operator: 44 operands: 37
34	ExprTuple	38, 39
35	Literal
36	ExprTuple	40, 41
37	ExprTuple	42, 43
38	Variable
39	Variable
40	Literal
41	Operation	operator: 44 operands: 45
42	Variable
43	Variable
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Literal

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶