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, n, x
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Ceil, Integer, Real

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(x, Conditional(Forall(instance_param_or_params = [n], instance_expr = Equals(Ceil(Add(x, n)), Add(Ceil(x), n)), domain = Integer), InSet(x, Real))))

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