Expression of type Lambda

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 ExprRange, IndexedVar, K, Lambda, Variable, m, n
from proveit.core_expr_types import n_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.logic import CartExp, Forall, SubsetEq
from proveit.numbers import Mult, NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(K, Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [n_1_to_m], instance_expr = SubsetEq(TensorProd(ExprRange(sub_expr1, CartExp(K, IndexedVar(n, sub_expr1)), one, m)), CartExp(K, Mult(n_1_to_m))), domain = NaturalPos), 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())

K \mapsto \left[\forall_{m \in \mathbb{N}^+}~\left[\forall_{n_{1}, n_{2}, \ldots, n_{m} \in \mathbb{N}^+}~\left(\left(K^{n_{1}} {\otimes}  K^{n_{2}} {\otimes}  \ldots {\otimes}  K^{n_{m}}\right) \subseteq K^{n_{1} \cdot  n_{2} \cdot  \ldots \cdot  n_{m}}\right)\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 43 body: 2
1	ExprTuple	43
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 42 body: 6
5	ExprTuple	42
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 33 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	42, 37
12	Lambda	parameters: 32 body: 13
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 38 operands: 25
22	ExprRange	lambda_map: 26 start_index: 41 end_index: 42
23	Literal
24	ExprTuple	27
25	ExprTuple	43, 28
26	Lambda	parameter: 47 body: 29
27	ExprRange	lambda_map: 30 start_index: 41 end_index: 42
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	Lambda	parameter: 47 body: 35
31	Literal
32	ExprTuple	36
33	Literal
34	ExprTuple	44, 37
35	Operation	operator: 38 operands: 39
36	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
37	Literal
38	Literal
39	ExprTuple	43, 44
40	Lambda	parameter: 47 body: 44
41	Literal
42	Variable
43	Variable
44	IndexedVar	variable: 45 index: 47
45	Variable
46	ExprTuple	47
47	Variable