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 Mod, ModAbs, Real, RealPos

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

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|_{\textup{mod}\thinspace b} = \left|a\right|_{\textup{mod}\thinspace b} \textrm{ if } a \in \mathbb{R} ,  b \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: 21 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: 13 operands: 12
9	Operation	operator: 13 operands: 21
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17, 23
13	Literal
14	ExprTuple	22, 18
15	Literal
16	ExprTuple	23, 19
17	Operation	operator: 20 operands: 21
18	Literal
19	Literal
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Variable