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Expression of type Lambda

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, Lambda, a, x, y
from proveit.logic import And, InSet
from proveit.numbers import Exp, Less, LessEq, Real, greater, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, x, y], Conditional(Less(Exp(x, a), Exp(y, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), And(LessEq(zero, x), Less(x, y)).with_total_ordering_style(), greater(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(a, x, y\right) \mapsto \left\{x^{a} < y^{a} \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  0 \leq x < y ,  a > 0\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple27, 33, 34
2Conditionalvalue: 3
condition: 4
3Operationoperator: 30
operands: 5
4Operationoperator: 21
operands: 6
5ExprTuple7, 8
6ExprTuple9, 10, 11, 12, 13
7Operationoperator: 15
operands: 14
8Operationoperator: 15
operands: 16
9Operationoperator: 19
operands: 17
10Operationoperator: 19
operands: 18
11Operationoperator: 19
operands: 20
12Operationoperator: 21
operands: 22
13Operationoperator: 30
operands: 23
14ExprTuple33, 27
15Literal
16ExprTuple34, 27
17ExprTuple27, 24
18ExprTuple33, 24
19Literal
20ExprTuple34, 24
21Literal
22ExprTuple25, 26
23ExprTuple32, 27
24Literal
25Operationoperator: 28
operands: 29
26Operationoperator: 30
operands: 31
27Variable
28Literal
29ExprTuple32, 33
30Literal
31ExprTuple33, 34
32Literal
33Variable
34Variable