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, InSet
from proveit.numbers import ModAbs, Real, RealPos, greater_eq, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, N], Conditional(greater_eq(ModAbs(subtract(a, b), N), subtract(ModAbs(a, N), ModAbs(b, 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} \geq \left(\left|a\right|_{\textup{mod}\thinspace N} - \left|b\right|_{\textup{mod}\thinspace N}\right) \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	31, 38, 37
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: 28 operands: 15
11	Operation	operator: 33 operands: 16
12	Operation	operator: 19 operands: 17
13	Operation	operator: 19 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21, 22
16	ExprTuple	23, 37
17	ExprTuple	31, 24
18	ExprTuple	38, 24
19	Literal
20	ExprTuple	37, 25
21	Operation	operator: 33 operands: 26
22	Operation	operator: 35 operand: 30
23	Operation	operator: 28 operands: 29
24	Literal
25	Literal
26	ExprTuple	31, 37
27	ExprTuple	30
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 33 operands: 34
31	Variable
32	Operation	operator: 35 operand: 38
33	Literal
34	ExprTuple	38, 37
35	Literal
36	ExprTuple	38
37	Variable
38	Variable