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, 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, z], Conditional(Forall(instance_param_or_params = [y], instance_expr = Equals(frac(Mult(x, y), Mult(x, z)), 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(x, z\right) \mapsto \left\{\forall_{y \in \mathbb{C}}~\left(\frac{x \cdot y}{x \cdot z} = \frac{y}{z}\right) \textrm{ if } x \in \mathbb{C}^{\neq 0} ,  z \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: 32 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 33 body: 12
9	Operation	operator: 20 operands: 13
10	Operation	operator: 20 operands: 14
11	ExprTuple	33
12	Conditional	value: 15 condition: 16
13	ExprTuple	34, 17
14	ExprTuple	35, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	33, 24
22	Operation	operator: 26 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	33, 35
28	Operation	operator: 31 operands: 30
29	Operation	operator: 31 operands: 32
30	ExprTuple	34, 33
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Variable
35	Variable