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, a, x, y
from proveit.logic import And, Equals, InSet
from proveit.numbers import Mult, Real

In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Mult(x, a), Mult(y, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), Equals(x, y)))

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(x \cdot a\right) = \left(y \cdot a\right) \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  x = y\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 19
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9, 10, 11
6Operationoperator: 13
operands: 12
7Operationoperator: 13
operands: 14
8Operationoperator: 17
operands: 15
9Operationoperator: 17
operands: 16
10Operationoperator: 17
operands: 18
11Operationoperator: 19
operands: 20
12ExprTuple23, 21
13Literal
14ExprTuple24, 21
15ExprTuple21, 22
16ExprTuple23, 22
17Literal
18ExprTuple24, 22
19Literal
20ExprTuple23, 24
21Variable
22Literal
23Variable
24Variable