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, LessEq, Mod, NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
sub_expr2 = Card(sub_expr1)
expr = Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = sub_expr1)), sub_expr2), domain = Integer, condition = LessEq(sub_expr2, 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\}| \leq N}~\left(|\left\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = |\{a~\ldotp \ldotp~b\}|\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: 38 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	40, 7
6	Lambda	parameters: 44 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, 26
13	Literal
14	ExprTuple	16, 17, 18
15	Operation	operator: 29 operand: 24
16	Operation	operator: 38 operands: 20
17	Operation	operator: 38 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24
20	ExprTuple	45, 25
21	ExprTuple	46, 25
22	Literal
23	ExprTuple	26, 40
24	Operation	operator: 27 operand: 31
25	Literal
26	Operation	operator: 29 operand: 42
27	Literal
28	ExprTuple	31
29	Literal
30	ExprTuple	42
31	Lambda	parameter: 41 body: 33
32	ExprTuple	41
33	Conditional	value: 34 condition: 35
34	Operation	operator: 36 operands: 37
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	41, 40
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Variable
42	Operation	operator: 43 operands: 44
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 ¶