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, 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, z], Conditional(Forall(instance_param_or_params = [y], instance_expr = Equals(frac(Mult(y, x), Mult(z, x)), frac(y, z)), domain = Complex), And(InSet(x, ComplexNonZero), InSet(z, 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(\left(x, z\right) \mapsto \left\{\forall_{y \in \mathbb{C}}~\left(\frac{y \cdot x}{z \cdot x} = \frac{y}{z}\right) \textrm{ if } x \in \mathbb{C}^{\neq 0} ,  z \in \mathbb{C}^{\neq 0}\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: 2 body: 3
2	ExprTuple	37, 36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 35 body: 14
11	Operation	operator: 22 operands: 15
12	Operation	operator: 22 operands: 16
13	ExprTuple	35
14	Conditional	value: 17 condition: 18
15	ExprTuple	37, 19
16	ExprTuple	36, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	35, 26
24	Operation	operator: 28 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	35, 36
30	Operation	operator: 33 operands: 32
31	Operation	operator: 33 operands: 34
32	ExprTuple	35, 37
33	Literal
34	ExprTuple	36, 37
35	Variable
36	Variable
37	Variable