Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 38 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 40 body: 11
9	Operation	operator: 28 operands: 12
10	Operation	operator: 28 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	41, 16
13	ExprTuple	42, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 39 operands: 25
22	Operation	operator: 36 operands: 26
23	Operation	operator: 28 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprTuple	30, 31
26	ExprTuple	32, 33
27	ExprTuple	43, 34
28	Literal
29	ExprTuple	44, 34
30	Operation	operator: 36 operands: 35
31	Operation	operator: 36 operands: 37
32	Operation	operator: 39 operands: 38
33	Operation	operator: 39 operands: 40
34	Literal
35	ExprTuple	41, 43
36	Literal
37	ExprTuple	42, 44
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43, 44
41	Variable
42	Variable
43	Variable
44	Variable