# from the theory of proveit.numbers.division¶

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 x, y
from proveit.logic import Equals, Forall, NotEquals
from proveit.numbers import Complex, Exp, Mult, Neg, frac, one, zero

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, y], instance_expr = Equals(frac(x, y), Mult(x, Exp(y, Neg(one)))), domain = Complex, condition = NotEquals(y, 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())

\forall_{x, y \in \mathbb{C}~|~y \neq 0}~\left(\frac{x}{y} = \left(x \cdot y^{-1}\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: 17
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14, 15
11Operationoperator: 16
operands: 17
12Operationoperator: 18
operands: 19
13Operationoperator: 21
operands: 20
14Operationoperator: 21
operands: 22
15Operationoperator: 23
operands: 24
16Literal
17ExprTuple26, 31
18Literal
19ExprTuple26, 25
20ExprTuple26, 27
21Literal
22ExprTuple31, 27
23Literal
24ExprTuple31, 28
25Operationoperator: 29
operands: 30
26Variable
27Literal
28Literal
29Literal
30ExprTuple31, 32
31Variable
32Operationoperator: 33
operand: 35
33Literal
34ExprTuple35
35Literal