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 a, b, c, d, e
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 = [a, d], instance_expr = Forall(instance_param_or_params = [b, c, e], instance_expr = Equals(Mult(frac(Mult(a, b), c), frac(d, Mult(b, e))), Mult(frac(a, c), frac(d, e))), 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_{a, d \in \mathbb{C}}~\left[\forall_{b, c, e \in \mathbb{C}^{\neq 0}}~\left(\left(\frac{a \cdot b}{c} \cdot \frac{d}{b \cdot e}\right) = \left(\frac{a}{c} \cdot \frac{d}{e}\right)\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	52, 48
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 22 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 13 body: 14
11	Operation	operator: 33 operands: 15
12	Operation	operator: 33 operands: 16
13	ExprTuple	53, 47, 54
14	Conditional	value: 17 condition: 18
15	ExprTuple	52, 19
16	ExprTuple	48, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27, 28
24	Operation	operator: 50 operands: 29
25	Operation	operator: 50 operands: 30
26	Operation	operator: 33 operands: 31
27	Operation	operator: 33 operands: 32
28	Operation	operator: 33 operands: 34
29	ExprTuple	35, 36
30	ExprTuple	37, 38
31	ExprTuple	53, 39
32	ExprTuple	47, 39
33	Literal
34	ExprTuple	54, 39
35	Operation	operator: 43 operands: 40
36	Operation	operator: 43 operands: 41
37	Operation	operator: 43 operands: 42
38	Operation	operator: 43 operands: 44
39	Literal
40	ExprTuple	45, 47
41	ExprTuple	48, 46
42	ExprTuple	52, 47
43	Literal
44	ExprTuple	48, 54
45	Operation	operator: 50 operands: 49
46	Operation	operator: 50 operands: 51
47	Variable
48	Variable
49	ExprTuple	52, 53
50	Literal
51	ExprTuple	53, 54
52	Variable
53	Variable
54	Variable