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, Lambda, 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 = Lambda([a, x, y], 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(a, x, y\right) \mapsto \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()

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

core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple28, 26, 27
2Conditionalvalue: 3
condition: 4
3Operationoperator: 23
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12, 13, 14
8Operationoperator: 16
operands: 15
9Operationoperator: 16
operands: 17
10Operationoperator: 20
operands: 18
11Operationoperator: 20
operands: 19
12Operationoperator: 20
operands: 21
13Operationoperator: 23
operands: 22
14Operationoperator: 23
operands: 24
15ExprTuple28, 26
16Literal
17ExprTuple28, 27
18ExprTuple28, 25
19ExprTuple26, 25
20Literal
21ExprTuple27, 25
22ExprTuple26, 27
23Literal
24ExprTuple28, 29
25Literal
26Variable
27Variable
28Variable
29Literal