Expression of type Forall

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 w, x, y, z
from proveit.logic import Equals, Forall, NotEquals
from proveit.numbers import Complex, frac, subtract

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [w, x, y, z], instance_expr = Equals(frac(subtract(w, x), subtract(y, z)), frac(subtract(x, w), subtract(z, y))), domain = Complex, condition = 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())

\forall_{w, x, y, z \in \mathbb{C}~|~y \neq z}~\left(\frac{w - x}{y - z} = \frac{x - w}{z - y}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	50, 48, 51, 49
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16, 17, 18
12	Operation	operator: 20 operands: 19
13	Operation	operator: 20 operands: 21
14	Operation	operator: 25 operands: 22
15	Operation	operator: 25 operands: 23
16	Operation	operator: 25 operands: 24
17	Operation	operator: 25 operands: 26
18	Operation	operator: 27 operands: 28
19	ExprTuple	29, 30
20	Literal
21	ExprTuple	31, 32
22	ExprTuple	50, 33
23	ExprTuple	48, 33
24	ExprTuple	51, 33
25	Literal
26	ExprTuple	49, 33
27	Literal
28	ExprTuple	51, 49
29	Operation	operator: 37 operands: 34
30	Operation	operator: 37 operands: 35
31	Operation	operator: 37 operands: 36
32	Operation	operator: 37 operands: 38
33	Literal
34	ExprTuple	50, 39
35	ExprTuple	51, 40
36	ExprTuple	48, 41
37	Literal
38	ExprTuple	49, 42
39	Operation	operator: 46 operand: 48
40	Operation	operator: 46 operand: 49
41	Operation	operator: 46 operand: 50
42	Operation	operator: 46 operand: 51
43	ExprTuple	48
44	ExprTuple	49
45	ExprTuple	50
46	Literal
47	ExprTuple	51
48	Variable
49	Variable
50	Variable
51	Variable