Expression of type Forall

from the theory of proveit.numbers.multiplication

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 b, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Mult, Natural

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [a_1_to_n, b], instance_expr = Equals(Mult(a_1_to_n, b), Mult(Mult(a_1_to_n), b)), domain = Complex), domain = Natural)

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_{n \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{n}, b \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n} \cdot b\right) = \left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \cdot b\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	parameter: 38 body: 4
3	ExprTuple	38
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 32 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	38, 11
10	Lambda	parameters: 23 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 30 operands: 23
20	Operation	operator: 30 operands: 24
21	ExprRange	lambda_map: 25 start_index: 37 end_index: 38
22	Operation	operator: 32 operands: 26
23	ExprTuple	34, 29
24	ExprTuple	27, 29
25	Lambda	parameter: 42 body: 28
26	ExprTuple	29, 35
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	Variable
30	Literal
31	ExprTuple	34
32	Literal
33	ExprTuple	39, 35
34	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
35	Literal
36	Lambda	parameter: 42 body: 39
37	Literal
38	Variable
39	IndexedVar	variable: 40 index: 42
40	Variable
41	ExprTuple	42
42	Variable