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Expression of type Conditional

from the theory of proveit.numbers.modular

In [1]:
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 And, Card, Equals, InSet, SetOfAll
from proveit.numbers import Integer, Interval, Mod, greater_eq
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = Conditional(Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = sub_expr1)), N), And(InSet(a, Integer), InSet(b, Integer), greater_eq(Card(sub_expr1), N)))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{|\left\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = N \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  |\{a~\ldotp \ldotp~b\}| \geq N\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 32
5Literal
6ExprTuple8, 9, 10
7Operationoperator: 21
operand: 16
8Operationoperator: 30
operands: 12
9Operationoperator: 30
operands: 13
10Operationoperator: 14
operands: 15
11ExprTuple16
12ExprTuple37, 17
13ExprTuple38, 17
14Literal
15ExprTuple32, 18
16Operationoperator: 19
operand: 23
17Literal
18Operationoperator: 21
operand: 34
19Literal
20ExprTuple23
21Literal
22ExprTuple34
23Lambdaparameter: 33
body: 25
24ExprTuple33
25Conditionalvalue: 26
condition: 27
26Operationoperator: 28
operands: 29
27Operationoperator: 30
operands: 31
28Literal
29ExprTuple33, 32
30Literal
31ExprTuple33, 34
32Variable
33Variable
34Operationoperator: 35
operands: 36
35Literal
36ExprTuple37, 38
37Variable
38Variable