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, Equals, InSet
from proveit.numbers import Mod, Real, RealPos

# build up the expression from sub-expressions
sub_expr1 = Mod(a, b)
expr = ExprTuple(Lambda([a, b], Conditional(Equals(Mod(sub_expr1, b), sub_expr1), And(InSet(a, Real), InSet(b, 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\right) \mapsto \left\{\left(\left(a ~\textup{mod}~ b\right) ~\textup{mod}~ b\right) = \left(a ~\textup{mod}~ b\right) \textrm{ if } a \in \mathbb{R} ,  b \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: 20 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 16
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 19 operands: 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	16, 22
13	ExprTuple	21, 17
14	Literal
15	ExprTuple	22, 18
16	Operation	operator: 19 operands: 20
17	Literal
18	Literal
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Variable