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, Equals, InSet
from proveit.numbers import LessEq, Min, Real

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

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) = y \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R} ,  y \leq x\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 13 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, 20
6	Literal
7	ExprTuple	9, 10, 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	21, 20
14	ExprTuple	21, 19
15	Literal
16	ExprTuple	20, 19
17	Literal
18	ExprTuple	20, 21
19	Literal
20	Variable
21	Variable