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Expression of type ExprTuple

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, ExprTuple, Lambda, a, c
from proveit.logic import And
from proveit.numbers import Abs, Less, Neg
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, c], Conditional(Less(Abs(a), c), And(Less(Neg(c), a), Less(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, c\right) \mapsto \left\{\left|a\right| < c \textrm{ if } \left(-c\right) < a ,  a < c\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 15
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 14
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 20
6Literal
7ExprTuple9, 10
8Operationoperator: 11
operand: 17
9Operationoperator: 14
operands: 13
10Operationoperator: 14
operands: 15
11Literal
12ExprTuple17
13ExprTuple16, 17
14Literal
15ExprTuple17, 20
16Operationoperator: 18
operand: 20
17Variable
18Literal
19ExprTuple20
20Variable