# 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, ExprTuple, Function, Lambda, Q, f
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.numbers import Mult

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = ExprTuple(Lambda(sub_expr1, Conditional(Mult(a_1_to_i, Function(f, sub_expr1), c_1_to_k), 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(\left(b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k} \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right..\right)

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 14
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 14
5Literal
6ExprTuple8, 9, 10
7Variable
8ExprRangelambda_map: 11
start_index: 22
end_index: 12
9Operationoperator: 13
operands: 14
10ExprRangelambda_map: 15
start_index: 22
end_index: 16
11Lambdaparameter: 28
body: 17
12Variable
13Variable
14ExprTuple18
15Lambdaparameter: 28
body: 19
16Variable
17IndexedVarvariable: 20
index: 28
18ExprRangelambda_map: 21
start_index: 22
end_index: 23
19IndexedVarvariable: 24
index: 28
20Variable
21Lambdaparameter: 28
body: 25
22Literal
23Variable
24Variable
25IndexedVarvariable: 26
index: 28
26Variable
27ExprTuple28
28Variable