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Expression of type ExprTuple

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, ExprTuple, Lambda, a, x, y
from proveit.logic import And, InSet
from proveit.numbers import Exp, LessEq, Real, greater, zero
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, x, y], Conditional(LessEq(Exp(x, a), Exp(y, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), And(LessEq(zero, x), LessEq(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(\left(a, x, y\right) \mapsto \left\{x^{a} \leq y^{a} \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  0 \leq x \leq y ,  a > 0\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: 2
body: 3
2ExprTuple29, 34, 35
3Conditionalvalue: 4
condition: 5
4Operationoperator: 31
operands: 6
5Operationoperator: 22
operands: 7
6ExprTuple8, 9
7ExprTuple10, 11, 12, 13, 14
8Operationoperator: 16
operands: 15
9Operationoperator: 16
operands: 17
10Operationoperator: 20
operands: 18
11Operationoperator: 20
operands: 19
12Operationoperator: 20
operands: 21
13Operationoperator: 22
operands: 23
14Operationoperator: 24
operands: 25
15ExprTuple34, 29
16Literal
17ExprTuple35, 29
18ExprTuple29, 26
19ExprTuple34, 26
20Literal
21ExprTuple35, 26
22Literal
23ExprTuple27, 28
24Literal
25ExprTuple33, 29
26Literal
27Operationoperator: 31
operands: 30
28Operationoperator: 31
operands: 32
29Variable
30ExprTuple33, 34
31Literal
32ExprTuple34, 35
33Literal
34Variable
35Variable