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 ComplexNonZero, Mult, frac

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [b, c, e], instance_expr = Equals(Mult(frac(a, Mult(b, c)), frac(Mult(c, d), e)), Mult(frac(a, b), frac(d, e))), domain = ComplexNonZero)

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_{b, c, e \in \mathbb{C}^{\neq 0}}~\left(\left(\frac{a}{b \cdot c} \cdot \frac{c \cdot d}{e}\right) = \left(\frac{a}{b} \cdot \frac{d}{e}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	40, 41, 36
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
12	Operation	operator: 38 operands: 17
13	Operation	operator: 38 operands: 18
14	Operation	operator: 21 operands: 19
15	Operation	operator: 21 operands: 20
16	Operation	operator: 21 operands: 22
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	ExprTuple	40, 27
20	ExprTuple	41, 27
21	Literal
22	ExprTuple	36, 27
23	Operation	operator: 31 operands: 28
24	Operation	operator: 31 operands: 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	Literal
28	ExprTuple	35, 33
29	ExprTuple	34, 36
30	ExprTuple	35, 40
31	Literal
32	ExprTuple	42, 36
33	Operation	operator: 38 operands: 37
34	Operation	operator: 38 operands: 39
35	Variable
36	Variable
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Variable
42	Variable