from the theory of proveit.numbers.ordering¶

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, ConditionalSet, x, y
from proveit.logic import Equals, Forall
from proveit.numbers import Max, Real, greater, greater_eq

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, y], instance_expr = Equals(Max(x, y), ConditionalSet(Conditional(x, greater_eq(x, y)), Conditional(y, greater(y, x)))), domain = Real)

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_{x, y \in \mathbb{R}}~\left({\rm Max}\left(x, y\right) = \left\{\begin{array}{ccc}x \textrm{ if } x \geq y \\ y \textrm{ if } y > x\end{array}\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: 29
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14
11Operationoperator: 15
operands: 29
12Operationoperator: 16
operands: 17
13Operationoperator: 19
operands: 18
14Operationoperator: 19
operands: 20
15Literal
16Literal
17ExprTuple21, 22
18ExprTuple30, 23
19Literal
20ExprTuple31, 23
21Conditionalvalue: 30
condition: 24
22Conditionalvalue: 31
condition: 25
23Literal
24Operationoperator: 26
operands: 27
25Operationoperator: 28
operands: 29
26Literal
27ExprTuple31, 30
28Literal
29ExprTuple30, 31
30Variable
31Variable