Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 13 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 17 operands: 7
5	Literal
6	ExprTuple	8, 27
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, 31
14	ExprTuple	27, 19
15	Literal
16	ExprTuple	31, 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	Literal
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	27, 28
26	Literal
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Variable
32	Literal