Expression of type Forall

from the theory of proveit.linear_algebra.tensors

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 K, i
from proveit.core_expr_types import V_1_to_i
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import Forall, InClass
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = Forall(instance_param_or_params = [K], instance_expr = Forall(instance_param_or_params = [i], instance_expr = Forall(instance_param_or_params = [V_1_to_i], instance_expr = InClass(TensorProd(V_1_to_i), sub_expr1), domain = sub_expr1), domain = NaturalPos))

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