Expression of type Lambda

from the theory of proveit.numbers.ordering

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

# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(Less(y, x), And(InSet(x, Real), InSet(y, Real), Not(LessEq(x, y)))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(x, y\right) \mapsto \left\{y < x \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R} ,  \lnot \left(x \leq y\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 19 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	21, 20
6	Literal
7	ExprTuple	8, 9, 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operand: 17
11	ExprTuple	20, 16
12	Literal
13	ExprTuple	21, 16
14	Literal
15	ExprTuple	17
16	Literal
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21
20	Variable
21	Variable