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, a, b
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Abs, Integer, Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(InSet(Mod(a, b), Interval(zero, subtract(Abs(b), one))), And(InSet(a, Integer), InSet(b, Integer), NotEquals(b, zero)))))

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\right) \mapsto \left\{\left(a ~\textup{mod}~ b\right) \in \{0~\ldotp \ldotp~\left|b\right| - 1\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  b \neq 0\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: 14 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 18 operands: 17
11	Operation	operator: 18 operands: 19
12	Operation	operator: 20 operands: 21
13	Literal
14	ExprTuple	23, 34
15	Literal
16	ExprTuple	25, 22
17	ExprTuple	23, 24
18	Literal
19	ExprTuple	34, 24
20	Literal
21	ExprTuple	34, 25
22	Operation	operator: 26 operands: 27
23	Variable
24	Literal
25	Literal
26	Literal
27	ExprTuple	28, 29
28	Operation	operator: 30 operand: 34
29	Operation	operator: 32 operand: 35
30	Literal
31	ExprTuple	34
32	Literal
33	ExprTuple	35
34	Variable
35	Literal