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
from proveit.numbers import Complex, ComplexNonZero, Mult, frac

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

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_{x, y \in \mathbb{C}}~\left[\forall_{z, w \in \mathbb{C}^{\neq 0}}~\left(\left(\frac{x}{z} \cdot \frac{y}{w}\right) = \frac{x \cdot y}{z \cdot w}\right)\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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 39 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 41 body: 12
10	Operation	operator: 29 operands: 13
11	Operation	operator: 29 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	42, 17
14	ExprTuple	43, 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	24, 25
22	Operation	operator: 40 operands: 26
23	Operation	operator: 37 operands: 27
24	Operation	operator: 29 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprTuple	31, 32
27	ExprTuple	33, 34
28	ExprTuple	44, 35
29	Literal
30	ExprTuple	45, 35
31	Operation	operator: 37 operands: 36
32	Operation	operator: 37 operands: 38
33	Operation	operator: 40 operands: 39
34	Operation	operator: 40 operands: 41
35	Literal
36	ExprTuple	42, 44
37	Literal
38	ExprTuple	43, 45
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	44, 45
42	Variable
43	Variable
44	Variable
45	Variable