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, InSet, NotEquals
from proveit.numbers import Complex, frac, subtract, zero

# build up the expression from sub-expressions
expr = Lambda([x, y, z], Conditional(Equals(frac(subtract(x, y), z), subtract(frac(x, z), frac(y, z))), And(InSet(x, Complex), InSet(y, Complex), InSet(z, Complex), NotEquals(z, zero))))

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, z\right) \mapsto \left\{\frac{x - y}{z} = \left(\frac{x}{z} - \frac{y}{z}\right) \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C} ,  z \in \mathbb{C} ,  z \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: 1 body: 2
1	ExprTuple	33, 39, 40
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14
9	Operation	operator: 37 operands: 15
10	Operation	operator: 28 operands: 16
11	Operation	operator: 19 operands: 17
12	Operation	operator: 19 operands: 18
13	Operation	operator: 19 operands: 20
14	Operation	operator: 21 operands: 22
15	ExprTuple	23, 40
16	ExprTuple	24, 25
17	ExprTuple	33, 26
18	ExprTuple	39, 26
19	Literal
20	ExprTuple	40, 26
21	Literal
22	ExprTuple	40, 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 37 operands: 30
25	Operation	operator: 35 operand: 34
26	Literal
27	Literal
28	Literal
29	ExprTuple	33, 32
30	ExprTuple	33, 40
31	ExprTuple	34
32	Operation	operator: 35 operand: 39
33	Variable
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	39
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Variable