Expression of type Forall

from the theory of proveit.numbers.divisibility

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, k
from proveit.logic import Forall, NotEquals
from proveit.numbers import Complex, Divides, Mult, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, k], instance_expr = Divides(a, b), domain = Complex, conditions = [Divides(Mult(k, a), Mult(k, b)), NotEquals(k, zero)])

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, b, k \in \mathbb{C}~|~\left(k \cdot a\right) \rvert \left(k \cdot b\right), k \neq 0}~\left(a \rvert b\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	31, 33, 32
5	Conditional	value: 6 condition: 7
6	Operation	operator: 20 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	31, 33
9	Literal
10	ExprTuple	11, 12, 13, 14, 15
11	Operation	operator: 18 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	Operation	operator: 20 operands: 21
15	Operation	operator: 22 operands: 23
16	ExprTuple	31, 24
17	ExprTuple	33, 24
18	Literal
19	ExprTuple	32, 24
20	Literal
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	32, 27
24	Literal
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	32, 31
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Variable
33	Variable