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Expression of type Lambda

from the theory of proveit.numbers.ordering

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, x, y
from proveit.logic import And, InSet, Not
from proveit.numbers import Less, LessEq, Real
In [2]:
# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(Not(LessEq(y, x)), And(InSet(x, Real), InSet(y, Real), 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\{\lnot \left(y \leq x\right) \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: 18
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operand: 8
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8
6Literal
7ExprTuple9, 10, 11
8Operationoperator: 12
operands: 13
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11Operationoperator: 17
operands: 18
12Literal
13ExprTuple21, 20
14ExprTuple20, 19
15Literal
16ExprTuple21, 19
17Literal
18ExprTuple20, 21
19Literal
20Variable
21Variable