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Expression of type ExprTuple

from the theory of proveit.numbers.number_sets.integers

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, b, x
from proveit.logic import And, InSet, NotInSet, Or
from proveit.numbers import Integer, Interval, Less
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, x], Conditional(Or(Less(x, a), Less(b, x)), And(InSet(a, Integer), InSet(b, Integer), InSet(x, Integer), NotInSet(x, Interval(a, b))))))
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, b, x\right) \mapsto \left\{\left(x < a\right) \lor \left(b < x\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  x \in \mathbb{Z} ,  x \notin \{a~\ldotp \ldotp~b\}\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: 2
body: 3
2ExprTuple30, 31, 26
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14, 15
10Operationoperator: 17
operands: 16
11Operationoperator: 17
operands: 18
12Operationoperator: 21
operands: 19
13Operationoperator: 21
operands: 20
14Operationoperator: 21
operands: 22
15Operationoperator: 23
operands: 24
16ExprTuple26, 30
17Literal
18ExprTuple31, 26
19ExprTuple30, 25
20ExprTuple31, 25
21Literal
22ExprTuple26, 25
23Literal
24ExprTuple26, 27
25Literal
26Variable
27Operationoperator: 28
operands: 29
28Literal
29ExprTuple30, 31
30Variable
31Variable