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

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

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(w, x, y, z\right) \mapsto \left\{\frac{w - x}{y - z} = \frac{x - w}{z - y} \textrm{ if } w \in \mathbb{C} ,  x \in \mathbb{C} ,  y \in \mathbb{C} ,  z \in \mathbb{C} ,  y \neq z\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	47, 45, 48, 46
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, 15
9	Operation	operator: 17 operands: 16
10	Operation	operator: 17 operands: 18
11	Operation	operator: 22 operands: 19
12	Operation	operator: 22 operands: 20
13	Operation	operator: 22 operands: 21
14	Operation	operator: 22 operands: 23
15	Operation	operator: 24 operands: 25
16	ExprTuple	26, 27
17	Literal
18	ExprTuple	28, 29
19	ExprTuple	47, 30
20	ExprTuple	45, 30
21	ExprTuple	48, 30
22	Literal
23	ExprTuple	46, 30
24	Literal
25	ExprTuple	48, 46
26	Operation	operator: 34 operands: 31
27	Operation	operator: 34 operands: 32
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	Literal
31	ExprTuple	47, 36
32	ExprTuple	48, 37
33	ExprTuple	45, 38
34	Literal
35	ExprTuple	46, 39
36	Operation	operator: 43 operand: 45
37	Operation	operator: 43 operand: 46
38	Operation	operator: 43 operand: 47
39	Operation	operator: 43 operand: 48
40	ExprTuple	45
41	ExprTuple	46
42	ExprTuple	47
43	Literal
44	ExprTuple	48
45	Variable
46	Variable
47	Variable
48	Variable