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, Forall, InSet
from proveit.numbers import Complex, ComplexNonZero, Mult, frac

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

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\{\forall_{z, w \in \mathbb{C}^{\neq 0}}~\left(\left(\frac{x}{z} \cdot \frac{y}{w}\right) = \frac{x \cdot y}{z \cdot w}\right) \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 37 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 18 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameters: 39 body: 10
8	Operation	operator: 27 operands: 11
9	Operation	operator: 27 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	40, 15
12	ExprTuple	41, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 38 operands: 24
21	Operation	operator: 35 operands: 25
22	Operation	operator: 27 operands: 26
23	Operation	operator: 27 operands: 28
24	ExprTuple	29, 30
25	ExprTuple	31, 32
26	ExprTuple	42, 33
27	Literal
28	ExprTuple	43, 33
29	Operation	operator: 35 operands: 34
30	Operation	operator: 35 operands: 36
31	Operation	operator: 38 operands: 37
32	Operation	operator: 38 operands: 39
33	Literal
34	ExprTuple	40, 42
35	Literal
36	ExprTuple	41, 43
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42, 43
40	Variable
41	Variable
42	Variable
43	Variable