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.
# import Expression classes needed to build the expression
from proveit import a, b
from proveit.logic import Equals, Forall
from proveit.numbers import Min, Mod, ModAbs, Neg, Real, RealPos

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = Equals(ModAbs(a, b), Min(Mod(a, b), Mod(Neg(a), b))), domains = [Real, 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())

\forall_{a \in \mathbb{R}, b \in \mathbb{R}^+}~\left(\left|a\right|_{\textup{mod}\thinspace b} = {\rm Min}\left(a ~\textup{mod}~ b, \left(-a\right) ~\textup{mod}~ b\right)\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 25
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14
11Operationoperator: 15
operands: 25
12Operationoperator: 16
operands: 17
13Operationoperator: 19
operands: 18
14Operationoperator: 19
operands: 20
15Literal
16Literal
17ExprTuple21, 22
18ExprTuple32, 23
19Literal
20ExprTuple29, 24
21Operationoperator: 26
operands: 25
22Operationoperator: 26
operands: 27
23Literal
24Literal
25ExprTuple32, 29
26Literal
27ExprTuple28, 29
28Operationoperator: 30
operand: 32
29Variable
30Literal
31ExprTuple32
32Variable