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Expression of type Conditional

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, 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 = 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\{|\{a~\ldotp \ldotp~b\}| = \left(b - a + 1\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a \leq b\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: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9, 10, 11
7Operationoperator: 12
operand: 20
8Operationoperator: 14
operands: 15
9Operationoperator: 17
operands: 16
10Operationoperator: 17
operands: 18
11Operationoperator: 19
operands: 25
12Literal
13ExprTuple20
14Literal
15ExprTuple28, 21, 22
16ExprTuple29, 23
17Literal
18ExprTuple28, 23
19Literal
20Operationoperator: 24
operands: 25
21Operationoperator: 26
operand: 29
22Literal
23Literal
24Literal
25ExprTuple29, 28
26Literal
27ExprTuple29
28Variable
29Variable