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, 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 = ExprTuple(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(\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..\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: 2 body: 3
2	ExprTuple	36, 35, 25
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 20 operands: 18
13	Operation	operator: 20 operands: 19
14	Operation	operator: 20 operands: 21
15	ExprTuple	22, 25
16	Literal
17	ExprTuple	23, 25
18	ExprTuple	36, 24
19	ExprTuple	35, 24
20	Literal
21	ExprTuple	25, 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	Variable
26	Literal
27	ExprTuple	36, 30
28	Literal
29	ExprTuple	35, 31
30	Operation	operator: 33 operand: 35
31	Operation	operator: 33 operand: 36
32	ExprTuple	35
33	Literal
34	ExprTuple	36
35	Variable
36	Variable