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Expression of type Lambda

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, Lambda, a, b
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Abs, Integer, Interval, ModAbs, one, subtract, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(InSet(ModAbs(a, b), Interval(zero, subtract(Abs(b), one))), And(InSet(a, Integer), InSet(b, Integer), NotEquals(b, zero))))
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(a, b\right) \mapsto \left\{\left|a\right|_{\textup{mod}\thinspace b} \in \{0~\ldotp \ldotp~\left|b\right| - 1\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  b \neq 0\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 13
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 17
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 8
5Literal
6ExprTuple9, 10, 11
7Operationoperator: 12
operands: 13
8Operationoperator: 14
operands: 15
9Operationoperator: 17
operands: 16
10Operationoperator: 17
operands: 18
11Operationoperator: 19
operands: 20
12Literal
13ExprTuple22, 33
14Literal
15ExprTuple24, 21
16ExprTuple22, 23
17Literal
18ExprTuple33, 23
19Literal
20ExprTuple33, 24
21Operationoperator: 25
operands: 26
22Variable
23Literal
24Literal
25Literal
26ExprTuple27, 28
27Operationoperator: 29
operand: 33
28Operationoperator: 31
operand: 34
29Literal
30ExprTuple33
31Literal
32ExprTuple34
33Variable
34Literal