a not-yet-official theorem 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 a, x, y
from proveit.logic import Equals, Forall
from proveit.numbers import Mult, Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, x, y], instance_expr = Equals(Mult(a, x), Mult(a, y)), domain = Natural, condition = 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: left_mult_eq matches stored_expr")

Passed sanity check: left_mult_eq matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{a, x, y \in \mathbb{N}~|~x = y}~\left(\left(a \cdot x\right) = \left(a \cdot y\right)\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple26, 28, 29
5Conditionalvalue: 6
condition: 7
6Operationoperator: 24
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple13, 14, 15, 16
11Operationoperator: 18
operands: 17
12Operationoperator: 18
operands: 19
13Operationoperator: 22
operands: 20
14Operationoperator: 22
operands: 21
15Operationoperator: 22
operands: 23
16Operationoperator: 24
operands: 25
17ExprTuple26, 28
18Literal
19ExprTuple26, 29
20ExprTuple26, 27
21ExprTuple28, 27
22Literal
23ExprTuple29, 27
24Literal
25ExprTuple28, 29
26Variable
27Literal
28Variable
29Variable