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, N, a, b
from proveit.logic import And, Equals, InSet
from proveit.numbers import ModAbs, Real, RealPos, subtract

# build up the expression from sub-expressions
expr = Lambda([a, b, N], Conditional(Equals(ModAbs(subtract(a, b), N), ModAbs(subtract(b, a), N)), And(InSet(a, Real), InSet(b, Real), InSet(N, 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, N\right) \mapsto \left\{\left|a - b\right|_{\textup{mod}\thinspace N} = \left|b - a\right|_{\textup{mod}\thinspace N} \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  N \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: 1 body: 2
1	ExprTuple	35, 34, 24
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
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 19 operands: 17
12	Operation	operator: 19 operands: 18
13	Operation	operator: 19 operands: 20
14	ExprTuple	21, 24
15	Literal
16	ExprTuple	22, 24
17	ExprTuple	35, 23
18	ExprTuple	34, 23
19	Literal
20	ExprTuple	24, 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	Variable
25	Literal
26	ExprTuple	35, 29
27	Literal
28	ExprTuple	34, 30
29	Operation	operator: 32 operand: 34
30	Operation	operator: 32 operand: 35
31	ExprTuple	34
32	Literal
33	ExprTuple	35
34	Variable
35	Variable