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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, b
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import RealPos, frac, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(InSet(frac(a, b), RealPos), And(InSet(a, RealPos), InSet(b, RealPos), NotEquals(b, 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, b\right) \mapsto \left\{\frac{a}{b} \in \mathbb{R}^+ \textrm{ if } a \in \mathbb{R}^+ ,  b \in \mathbb{R}^+ ,  b \neq 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: 12
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 14
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 19
5Literal
6ExprTuple8, 9, 10
7Operationoperator: 11
operands: 12
8Operationoperator: 14
operands: 13
9Operationoperator: 14
operands: 15
10Operationoperator: 16
operands: 17
11Literal
12ExprTuple18, 20
13ExprTuple18, 19
14Literal
15ExprTuple20, 19
16Literal
17ExprTuple20, 21
18Variable
19Literal
20Variable
21Literal