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, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import LessEq, ModAbs, Real, RealPos, frac, two, zero

# build up the expression from sub-expressions
expr = Lambda([x, N], Conditional(Equals(ModAbs(x, N), x), And(InSet(x, Real), InSet(N, RealPos), And(LessEq(zero, x), LessEq(x, frac(N, two))).with_total_ordering_style())))

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, N\right) \mapsto \left\{\left|x\right|_{\textup{mod}\thinspace N} = x \textrm{ if } x \in \mathbb{R} ,  N \in \mathbb{R}^+ ,  0 \leq x \leq \frac{N}{2}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 12 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 16 operands: 6
4	Literal
5	ExprTuple	7, 26
6	ExprTuple	8, 9, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 14 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	Literal
12	ExprTuple	26, 30
13	ExprTuple	26, 18
14	Literal
15	ExprTuple	30, 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	Literal
20	Operation	operator: 23 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	26, 27
25	Literal
26	Variable
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Literal