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Expression of type Card

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 N, a, b, c, x
from proveit.logic import Card, SetOfAll
from proveit.numbers import Add, Interval, Mod
In [2]:
# build up the expression from sub-expressions
expr = Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(x, c), N), domain = Interval(a, b)))
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 + c\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}|
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Operationoperator: 4
operand: 6
4Literal
5ExprTuple6
6Lambdaparameter: 22
body: 8
7ExprTuple22
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 16
13Literal
14ExprTuple22, 17
15Operationoperator: 18
operands: 19
16Variable
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple22, 23
20Literal
21ExprTuple24, 25
22Variable
23Variable
24Variable
25Variable