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 Conditional, ExprRange, IndexedVar, K, Lambda, V, Variable, i
from proveit.core_expr_types import V_1_to_i, a_1_to_i
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, Forall, InClass, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [V_1_to_i]
expr = Lambda(sub_expr2, Conditional(Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(TensorProd(a_1_to_i), TensorProd(V_1_to_i)), domains = sub_expr2), And(ExprRange(sub_expr1, InClass(IndexedVar(V, sub_expr1), VecSpaces(K)), one, i))))

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())

\left(V_{1}, V_{2}, \ldots, V_{i}\right) \mapsto \left\{\forall_{\left(a_{1} \in V_{1}\right), \left(a_{2} \in V_{2}\right), \ldots, \left(a_{i} \in V_{i}\right)}~\left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}\right) \in \left(V_{1} {\otimes}  V_{2} {\otimes}  \ldots {\otimes}  V_{i}\right)\right) \textrm{ if } \left(V_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \left(V_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \ldots \land  \left(V_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\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	parameters: 25 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 15 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8
7	Lambda	parameters: 23 body: 9
8	ExprRange	lambda_map: 10 start_index: 35 end_index: 36
9	Conditional	value: 11 condition: 12
10	Lambda	parameter: 44 body: 13
11	Operation	operator: 37 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21
17	Literal
18	ExprTuple	40, 22
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	ExprRange	lambda_map: 26 start_index: 35 end_index: 36
22	Operation	operator: 27 operand: 32
23	ExprTuple	29
24	Literal
25	ExprTuple	30
26	Lambda	parameter: 44 body: 31
27	Literal
28	ExprTuple	32
29	ExprRange	lambda_map: 33 start_index: 35 end_index: 36
30	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
31	Operation	operator: 37 operands: 38
32	Variable
33	Lambda	parameter: 44 body: 39
34	Lambda	parameter: 44 body: 40
35	Literal
36	Variable
37	Literal
38	ExprTuple	39, 40
39	IndexedVar	variable: 41 index: 44
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable