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Expression of type Lambda

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, 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 = 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(x, y\right) \mapsto \left\{\frac{a}{x} < \frac{a}{y} \textrm{ if } x \in \mathbb{R}^+ ,  y \in \mathbb{R}^+ ,  x < y\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 19
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 18
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 8
5Literal
6ExprTuple9, 10, 11
7Operationoperator: 13
operands: 12
8Operationoperator: 13
operands: 14
9Operationoperator: 16
operands: 15
10Operationoperator: 16
operands: 17
11Operationoperator: 18
operands: 19
12ExprTuple20, 22
13Literal
14ExprTuple20, 23
15ExprTuple22, 21
16Literal
17ExprTuple23, 21
18Literal
19ExprTuple22, 23
20Variable
21Literal
22Variable
23Variable