Expression of type Lambda

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

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Forall(instance_param_or_params = [n], instance_expr = Equals(Floor(Add(x, n)), Add(Floor(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())

x \mapsto \left\{\forall_{n \in \mathbb{Z}}~\left(\left\lfloor x + n\right\rfloor = \left(\left\lfloor x\right\rfloor + n\right)\right) \textrm{ if } x \in \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 29 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 15 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	29, 8
7	Lambda	parameter: 28 body: 10
8	Literal
9	ExprTuple	28
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	28, 19
17	Operation	operator: 26 operand: 22
18	Operation	operator: 24 operands: 21
19	Literal
20	ExprTuple	22
21	ExprTuple	23, 28
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	29, 28
26	Literal
27	ExprTuple	29
28	Variable
29	Variable