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Expression of type Conditional

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, a, b, c
from proveit.logic import And, InSet
from proveit.numbers import Abs, LessEq, Max, Real
In [2]:
# build up the expression from sub-expressions
expr = Conditional(LessEq(Abs(a), Max(Abs(b), Abs(c))), And(InSet(a, Real), InSet(b, Real), InSet(c, Real), 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())
\left\{\left|a\right| \leq {\rm Max}\left(\left|b\right|, \left|c\right|\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  c \in \mathbb{R} ,  b \leq a \leq c\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 29
operands: 3
2Operationoperator: 18
operands: 4
3ExprTuple5, 6
4ExprTuple7, 8, 9, 10
5Operationoperator: 26
operand: 32
6Operationoperator: 12
operands: 13
7Operationoperator: 16
operands: 14
8Operationoperator: 16
operands: 15
9Operationoperator: 16
operands: 17
10Operationoperator: 18
operands: 19
11ExprTuple32
12Literal
13ExprTuple20, 21
14ExprTuple32, 22
15ExprTuple31, 22
16Literal
17ExprTuple33, 22
18Literal
19ExprTuple23, 24
20Operationoperator: 26
operand: 31
21Operationoperator: 26
operand: 33
22Literal
23Operationoperator: 29
operands: 28
24Operationoperator: 29
operands: 30
25ExprTuple31
26Literal
27ExprTuple33
28ExprTuple31, 32
29Literal
30ExprTuple32, 33
31Variable
32Variable
33Variable