Expression of type Lambda

from the theory of proveit.numbers.modular

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, a, b
from proveit.logic import And, Equals, InSet
from proveit.numbers import Integer, Mod, ZeroSet, zero

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(InSet(Mod(a, b), ZeroSet), And(InSet(a, Integer), InSet(b, Integer), Equals(a, zero))))

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(a, b\right) \mapsto \left\{\left(a ~\textup{mod}~ b\right) \in \left\{0\right\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a = 0\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: 17 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 14 operand: 24
9	Operation	operator: 17 operands: 16
10	Operation	operator: 17 operands: 18
11	Operation	operator: 19 operands: 20
12	Literal
13	ExprTuple	23, 21
14	Literal
15	ExprTuple	24
16	ExprTuple	23, 22
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Variable
22	Literal
23	Variable
24	Literal