Expression of type ExprTuple

from the theory of proveit.numbers.rounding

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, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Ceil, Floor, Real, Round, subtract

# build up the expression from sub-expressions
sub_expr1 = Ceil(x)
expr = ExprTuple(Lambda(x, Conditional(Equals(Round(x), sub_expr1), And(InSet(x, Real), Equals(subtract(x, Floor(x)), subtract(sub_expr1, x))))))

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(x \mapsto \left\{round\left(x\right) = \left\lceil x\right\rceil \textrm{ if } x \in \mathbb{R} ,  \left(x - \left\lfloor x\right\rfloor\right) = \left(\left\lceil x\right\rceil - x\right)\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	parameter: 31 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 14 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 23
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operand: 31
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	Literal
13	ExprTuple	31, 16
14	Literal
15	ExprTuple	17, 18
16	Literal
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	31, 22
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 27 operand: 28
23	Operation	operator: 26 operand: 31
24	Operation	operator: 27 operand: 31
25	ExprTuple	28
26	Literal
27	Literal
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Variable