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Expression of type Lambda

from the theory of proveit.numbers.negation

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, Equals, InSet
from proveit.numbers import Add, Complex, Neg, subtract
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Neg(Add(a, b)), subtract(Neg(a), b)), And(InSet(a, Complex), InSet(b, Complex))))
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\{\left(-\left(a + b\right)\right) = \left(-a - b\right) \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 22
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple10, 11
8Operationoperator: 24
operand: 17
9Operationoperator: 21
operands: 13
10Operationoperator: 15
operands: 14
11Operationoperator: 15
operands: 16
12ExprTuple17
13ExprTuple18, 19
14ExprTuple26, 20
15Literal
16ExprTuple27, 20
17Operationoperator: 21
operands: 22
18Operationoperator: 24
operand: 26
19Operationoperator: 24
operand: 27
20Literal
21Literal
22ExprTuple26, 27
23ExprTuple26
24Literal
25ExprTuple27
26Variable
27Variable