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Expression of type Conditional

from the theory of proveit.numbers.exponentiation

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 Exp, Less, LessEq, Real, zero
In [2]:
# build up the expression from sub-expressions
expr = Conditional(LessEq(Exp(y, a), Exp(x, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), And(Less(zero, x), LessEq(x, y)).with_total_ordering_style(), Less(a, zero)))
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\{y^{a} \leq x^{a} \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  0 < x \leq y ,  a < 0\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: 28
operands: 3
2Operationoperator: 19
operands: 4
3ExprTuple5, 6
4ExprTuple7, 8, 9, 10, 11
5Operationoperator: 13
operands: 12
6Operationoperator: 13
operands: 14
7Operationoperator: 17
operands: 15
8Operationoperator: 17
operands: 16
9Operationoperator: 17
operands: 18
10Operationoperator: 19
operands: 20
11Operationoperator: 26
operands: 21
12ExprTuple32, 25
13Literal
14ExprTuple31, 25
15ExprTuple25, 22
16ExprTuple31, 22
17Literal
18ExprTuple32, 22
19Literal
20ExprTuple23, 24
21ExprTuple25, 30
22Literal
23Operationoperator: 26
operands: 27
24Operationoperator: 28
operands: 29
25Variable
26Literal
27ExprTuple30, 31
28Literal
29ExprTuple31, 32
30Literal
31Variable
32Variable