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Expression of type Lambda

from the theory of proveit.numbers.multiplication

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 And, InSet
from proveit.numbers import LessEq, Mult, Real, greater_eq, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, x, y], Conditional(greater_eq(Mult(x, a), Mult(y, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), LessEq(x, y), LessEq(a, zero))))
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())
\left(a, x, y\right) \mapsto \left\{\left(x \cdot a\right) \geq \left(y \cdot a\right) \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  x \leq y ,  a \leq 0\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple28, 26, 27
2Conditionalvalue: 3
condition: 4
3Operationoperator: 23
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12, 13, 14
8Operationoperator: 16
operands: 15
9Operationoperator: 16
operands: 17
10Operationoperator: 20
operands: 18
11Operationoperator: 20
operands: 19
12Operationoperator: 20
operands: 21
13Operationoperator: 23
operands: 22
14Operationoperator: 23
operands: 24
15ExprTuple27, 28
16Literal
17ExprTuple26, 28
18ExprTuple28, 25
19ExprTuple26, 25
20Literal
21ExprTuple27, 25
22ExprTuple26, 27
23Literal
24ExprTuple28, 29
25Literal
26Variable
27Variable
28Variable
29Literal