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Expression of type Lambda

from the theory of proveit.numbers.division

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, a, x, y
from proveit.logic import Forall, InSet
from proveit.numbers import LessEq, RealNeg, RealNonNeg, frac, greater_eq
In [2]:
# build up the expression from sub-expressions
expr = Lambda(a, Conditional(Forall(instance_param_or_params = [x, y], instance_expr = greater_eq(frac(a, x), frac(a, y)), domain = RealNeg, condition = LessEq(x, y)), InSet(a, RealNonNeg)))
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())
a \mapsto \left\{\forall_{x, y \in \mathbb{R}^-~|~x \leq y}~\left(\frac{a}{x} \geq \frac{a}{y}\right) \textrm{ if } a \in \mathbb{R}^{\ge 0}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 29
body: 2
1ExprTuple29
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 25
operands: 7
5Literal
6ExprTuple8
7ExprTuple29, 9
8Lambdaparameters: 28
body: 10
9Literal
10Conditionalvalue: 11
condition: 12
11Operationoperator: 27
operands: 13
12Operationoperator: 14
operands: 15
13ExprTuple16, 17
14Literal
15ExprTuple18, 19, 20
16Operationoperator: 22
operands: 21
17Operationoperator: 22
operands: 23
18Operationoperator: 25
operands: 24
19Operationoperator: 25
operands: 26
20Operationoperator: 27
operands: 28
21ExprTuple29, 32
22Literal
23ExprTuple29, 31
24ExprTuple31, 30
25Literal
26ExprTuple32, 30
27Literal
28ExprTuple31, 32
29Variable
30Literal
31Variable
32Variable