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, w, x, y, z
from proveit.logic import And, Equals, InSet
from proveit.numbers import ComplexNonZero, Mult, frac

# build up the expression from sub-expressions
expr = Lambda([z, w], Conditional(Equals(Mult(frac(x, z), frac(y, w)), frac(Mult(x, y), Mult(z, w))), And(InSet(z, ComplexNonZero), InSet(w, ComplexNonZero))))

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(z, w\right) \mapsto \left\{\left(\frac{x}{z} \cdot \frac{y}{w}\right) = \frac{x \cdot y}{z \cdot w} \textrm{ if } z \in \mathbb{C}^{\neq 0} ,  w \in \mathbb{C}^{\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: 27 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
8	Operation	operator: 26 operands: 12
9	Operation	operator: 23 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17, 18
13	ExprTuple	19, 20
14	ExprTuple	30, 21
15	Literal
16	ExprTuple	31, 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	Literal
22	ExprTuple	28, 30
23	Literal
24	ExprTuple	29, 31
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Variable
29	Variable
30	Variable
31	Variable