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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
from proveit.logic import And, Card, Equals, InSet
from proveit.numbers import Add, Integer, Interval, LessEq, Neg, one
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(Equals(Card(Interval(a, b)), Add(b, Neg(a), one)), And(InSet(a, Integer), InSet(b, Integer), LessEq(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\right) \mapsto \left\{|\{a~\ldotp \ldotp~b\}| = \left(b - a + 1\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a \leq 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: 27
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13
9Operationoperator: 14
operand: 22
10Operationoperator: 16
operands: 17
11Operationoperator: 19
operands: 18
12Operationoperator: 19
operands: 20
13Operationoperator: 21
operands: 27
14Literal
15ExprTuple22
16Literal
17ExprTuple30, 23, 24
18ExprTuple31, 25
19Literal
20ExprTuple30, 25
21Literal
22Operationoperator: 26
operands: 27
23Operationoperator: 28
operand: 31
24Literal
25Literal
26Literal
27ExprTuple31, 30
28Literal
29ExprTuple31
30Variable
31Variable