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 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 = 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(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..

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameters: 13
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 13
4Literal
5ExprTuple7, 8, 9
6Variable
7ExprRangelambda_map: 10
start_index: 21
end_index: 11
8Operationoperator: 12
operands: 13
9ExprRangelambda_map: 14
start_index: 21
end_index: 15
10Lambdaparameter: 27
body: 16
11Variable
12Variable
13ExprTuple17
14Lambdaparameter: 27
body: 18
15Variable
16IndexedVarvariable: 19
index: 27
17ExprRangelambda_map: 20
start_index: 21
end_index: 22
18IndexedVarvariable: 23
index: 27
19Variable
20Lambdaparameter: 27
body: 24
21Literal
22Variable
23Variable
24IndexedVarvariable: 25
index: 27
25Variable
26ExprTuple27
27Variable