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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, Equals, InSet
from proveit.numbers import Mod, Real, RealPos
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mod(a, b)
expr = Lambda([a, b], Conditional(Equals(Mod(sub_expr1, b), sub_expr1), And(InSet(a, Real), InSet(b, RealPos))))
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(\left(a ~\textup{mod}~ b\right) ~\textup{mod}~ b\right) = \left(a ~\textup{mod}~ b\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R}^+\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 19
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 15
6Literal
7ExprTuple9, 10
8Operationoperator: 18
operands: 11
9Operationoperator: 13
operands: 12
10Operationoperator: 13
operands: 14
11ExprTuple15, 21
12ExprTuple20, 16
13Literal
14ExprTuple21, 17
15Operationoperator: 18
operands: 19
16Literal
17Literal
18Literal
19ExprTuple20, 21
20Variable
21Variable