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.
# import Expression classes needed to build the expression
from proveit import Conditional, Function, Lambda, Q, f
from proveit.core_expr_types import b_1_to_j
from proveit.logic import InSet
from proveit.numbers import Complex

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = Lambda(sub_expr1, Conditional(InSet(Function(f, sub_expr1), Complex), Function(Q, sub_expr1)))

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(b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \in \mathbb{C} \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 10
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 10
4Literal
5ExprTuple7, 8
6Variable
7Operationoperator: 9
operands: 10
8Literal
9Variable
10ExprTuple11
11ExprRangelambda_map: 12
start_index: 13
end_index: 14
12Lambdaparameter: 18
body: 15
13Literal
14Variable
15IndexedVarvariable: 16
index: 18
16Variable
17ExprTuple18
18Variable