Expression of type Lambda

from the theory of proveit.numbers.divisibility

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, z
from proveit.logic import And
from proveit.numbers import Add, Divides

# build up the expression from sub-expressions
expr = Lambda([x, y, z], Conditional(Divides(x, Add(y, z)), And(Divides(x, y), Divides(x, z))))

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, z\right) \mapsto \left\{x \rvert \left(y + z\right) \textrm{ if } x \rvert y ,  x \rvert z\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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