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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, one
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, x, y], Conditional(LessEq(Exp(a, x), Exp(a, y)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), greater(a, one), LessEq(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(\left(a, x, y\right) \mapsto \left\{a^{x} \leq a^{y} \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  a > 1 ,  x \leq y\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, 30, 31
3Conditionalvalue: 4
condition: 5
4Operationoperator: 25
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13, 14, 15
9Operationoperator: 17
operands: 16
10Operationoperator: 17
operands: 18
11Operationoperator: 21
operands: 19
12Operationoperator: 21
operands: 20
13Operationoperator: 21
operands: 22
14Operationoperator: 23
operands: 24
15Operationoperator: 25
operands: 26
16ExprTuple29, 30
17Literal
18ExprTuple29, 31
19ExprTuple29, 27
20ExprTuple30, 27
21Literal
22ExprTuple31, 27
23Literal
24ExprTuple28, 29
25Literal
26ExprTuple30, 31
27Literal
28Literal
29Variable
30Variable
31Variable