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Expression of type Lambda

from the theory of proveit.numbers.rounding

In [1]:
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, x
from proveit.logic import InSet
from proveit.numbers import Floor, Less, Real, one, subtract
In [2]:
# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Less(subtract(x, Floor(x)), one), InSet(x, Real)))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
x \mapsto \left\{\left(x - \left\lfloor x\right\rfloor\right) < 1 \textrm{ if } x \in \mathbb{R}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 19
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple19, 10
8Operationoperator: 11
operands: 12
9Literal
10Literal
11Literal
12ExprTuple19, 13
13Operationoperator: 14
operand: 16
14Literal
15ExprTuple16
16Operationoperator: 17
operand: 19
17Literal
18ExprTuple19
19Variable