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, 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 = Lambda(N, 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())

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

Expression of type Lambda¶

from the theory of proveit.numbers.modular¶

Expression of type Lambda ¶

from the theory of proveit.numbers.modular ¶