Expression of type Lambda

from the theory of proveit.numbers.division

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, x, y
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, Neg, frac, one, zero

# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(Equals(frac(x, y), Mult(x, Exp(y, Neg(one)))), And(InSet(x, Complex), InSet(y, Complex), NotEquals(y, zero))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(x, y\right) \mapsto \left\{\frac{x}{y} = \left(x \cdot y^{-1}\right) \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C} ,  y \neq 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 14 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 18 operands: 17
11	Operation	operator: 18 operands: 19
12	Operation	operator: 20 operands: 21
13	Literal
14	ExprTuple	23, 28
15	Literal
16	ExprTuple	23, 22
17	ExprTuple	23, 24
18	Literal
19	ExprTuple	28, 24
20	Literal
21	ExprTuple	28, 25
22	Operation	operator: 26 operands: 27
23	Variable
24	Literal
25	Literal
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Literal