# 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, InSet, NotEquals
from proveit.numbers import Mult, Real, zero

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

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(a \cdot x\right) \neq \left(a \cdot y\right) \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  x \neq y ,  a \neq 0\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: 21
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9, 10, 11, 12
6Operationoperator: 14
operands: 13
7Operationoperator: 14
operands: 15
8Operationoperator: 18
operands: 16
9Operationoperator: 18
operands: 17
10Operationoperator: 18
operands: 19
11Operationoperator: 21
operands: 20
12Operationoperator: 21
operands: 22
13ExprTuple26, 24
14Literal
15ExprTuple26, 25
16ExprTuple26, 23
17ExprTuple24, 23
18Literal
19ExprTuple25, 23
20ExprTuple24, 25
21Literal
22ExprTuple26, 27
23Literal
24Variable
25Variable
26Variable
27Literal