# from the theory of proveit.numbers.absolute_value¶

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, c
from proveit.logic import And, Forall
from proveit.numbers import Abs, LessEq, Max, Real

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = LessEq(Abs(a), Max(Abs(b), Abs(c))), domain = Real, condition = And(LessEq(b, a), LessEq(a, c)).with_total_ordering_style())

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, b, c \in \mathbb{R}~|~b \leq a \leq c}~\left(\left|a\right| \leq {\rm Max}\left(\left|b\right|, \left|c\right|\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: 4
body: 5
4ExprTuple37, 36, 38
5Conditionalvalue: 6
condition: 7
6Operationoperator: 34
operands: 8
7Operationoperator: 23
operands: 9
8ExprTuple10, 11
9ExprTuple12, 13, 14, 15
10Operationoperator: 31
operand: 37
11Operationoperator: 17
operands: 18
12Operationoperator: 21
operands: 19
13Operationoperator: 21
operands: 20
14Operationoperator: 21
operands: 22
15Operationoperator: 23
operands: 24
16ExprTuple37
17Literal
18ExprTuple25, 26
19ExprTuple37, 27
20ExprTuple36, 27
21Literal
22ExprTuple38, 27
23Literal
24ExprTuple28, 29
25Operationoperator: 31
operand: 36
26Operationoperator: 31
operand: 38
27Literal
28Operationoperator: 34
operands: 33
29Operationoperator: 34
operands: 35
30ExprTuple36
31Literal
32ExprTuple38
33ExprTuple36, 37
34Literal
35ExprTuple37, 38
36Variable
37Variable
38Variable