logo

Expression of type Conditional

from the theory of proveit.numbers.division

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, x, y
from proveit.logic import And, InSet
from proveit.numbers import Less, RealNeg, frac
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Less(frac(a, x), frac(a, y)), And(InSet(a, RealNeg), InSet(x, RealNeg), InSet(y, RealNeg), Less(x, y)))
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\{\frac{a}{x} < \frac{a}{y} \textrm{ if } a \in \mathbb{R}^- ,  x \in \mathbb{R}^- ,  y \in \mathbb{R}^- ,  x < y\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: 19
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9, 10, 11
6Operationoperator: 13
operands: 12
7Operationoperator: 13
operands: 14
8Operationoperator: 17
operands: 15
9Operationoperator: 17
operands: 16
10Operationoperator: 17
operands: 18
11Operationoperator: 19
operands: 20
12ExprTuple21, 23
13Literal
14ExprTuple21, 24
15ExprTuple21, 22
16ExprTuple23, 22
17Literal
18ExprTuple24, 22
19Literal
20ExprTuple23, 24
21Variable
22Literal
23Variable
24Variable