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Expression of type ExprTuple

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, ExprTuple, Lambda, a, x, y
from proveit.logic import And, InSet
from proveit.numbers import Less, RealPos, frac
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y], Conditional(Less(frac(a, x), frac(a, y)), And(InSet(x, RealPos), InSet(y, RealPos), 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(\left(x, y\right) \mapsto \left\{\frac{a}{x} < \frac{a}{y} \textrm{ if } x \in \mathbb{R}^+ ,  y \in \mathbb{R}^+ ,  x < 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: 20
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 19
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12
8Operationoperator: 14
operands: 13
9Operationoperator: 14
operands: 15
10Operationoperator: 17
operands: 16
11Operationoperator: 17
operands: 18
12Operationoperator: 19
operands: 20
13ExprTuple21, 23
14Literal
15ExprTuple21, 24
16ExprTuple23, 22
17Literal
18ExprTuple24, 22
19Literal
20ExprTuple23, 24
21Variable
22Literal
23Variable
24Variable