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, 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 = ExprTuple(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(\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..\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: 2
body: 3
2ExprTuple29, 27, 28
3Conditionalvalue: 4
condition: 5
4Operationoperator: 24
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13, 14, 15
9Operationoperator: 17
operands: 16
10Operationoperator: 17
operands: 18
11Operationoperator: 21
operands: 19
12Operationoperator: 21
operands: 20
13Operationoperator: 21
operands: 22
14Operationoperator: 24
operands: 23
15Operationoperator: 24
operands: 25
16ExprTuple29, 27
17Literal
18ExprTuple29, 28
19ExprTuple29, 26
20ExprTuple27, 26
21Literal
22ExprTuple28, 26
23ExprTuple27, 28
24Literal
25ExprTuple29, 30
26Literal
27Variable
28Variable
29Variable
30Literal