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, c
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Abs, Add, LessEq, Mod, ModAbs, Real, subtract, zero

# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(LessEq(ModAbs(subtract(Mod(Add(b, a), c), b), c), Abs(a)), And(InSet(a, Real), InSet(b, Real), InSet(c, Real), NotEquals(c, 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, c\right) \mapsto \left\{\left|\left(\left(b + a\right) ~\textup{mod}~ c\right) - b\right|_{\textup{mod}\thinspace c} \leq \left|a\right| \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  c \in \mathbb{R} ,  c \neq 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: 1 body: 2
1	ExprTuple	40, 39, 36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operand: 40
11	Operation	operator: 21 operands: 19
12	Operation	operator: 21 operands: 20
13	Operation	operator: 21 operands: 22
14	Operation	operator: 23 operands: 24
15	Literal
16	ExprTuple	25, 36
17	Literal
18	ExprTuple	40
19	ExprTuple	40, 26
20	ExprTuple	39, 26
21	Literal
22	ExprTuple	36, 26
23	Literal
24	ExprTuple	36, 27
25	Operation	operator: 37 operands: 28
26	Literal
27	Literal
28	ExprTuple	29, 30
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operand: 39
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	39
35	Operation	operator: 37 operands: 38
36	Variable
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Variable