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 Abs, LessEq, ModAbs, Real, RealPos, frac, two

# build up the expression from sub-expressions
sub_expr1 = Abs(x)
expr = Lambda([x, N], Conditional(Equals(ModAbs(x, N), sub_expr1), And(InSet(x, Real), InSet(N, RealPos), LessEq(sub_expr1, frac(N, two)))))

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} = \left|x\right| \textrm{ if } x \in \mathbb{R} ,  N \in \mathbb{R}^+ ,  \left|x\right| \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: 13 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, 21
6	Literal
7	ExprTuple	9, 10, 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	27, 28
14	ExprTuple	27, 19
15	Literal
16	ExprTuple	28, 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	Literal
21	Operation	operator: 23 operand: 27
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Variable
29	Literal