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, ConditionalSet, Lambda, x, y
from proveit.logic import And, Equals, InSet
from proveit.numbers import Less, LessEq, Min, Real

# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(Equals(Min(x, y), ConditionalSet(Conditional(x, LessEq(x, y)), Conditional(y, Less(y, x)))), And(InSet(x, Real), InSet(y, Real))))

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\{{\rm Min}\left(x, y\right) = \left\{\begin{array}{ccc}x \textrm{ if } x \leq y \\ y \textrm{ if } y < x\end{array}\right.. \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 24 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operands: 24
9	Operation	operator: 13 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Literal
13	Literal
14	ExprTuple	18, 19
15	ExprTuple	28, 20
16	Literal
17	ExprTuple	27, 20
18	Conditional	value: 28 condition: 21
19	Conditional	value: 27 condition: 22
20	Literal
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	28, 27
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Variable