Expression of type And

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, U, V, Variable, W, i, k
from proveit.linear_algebra import VecSpaces
from proveit.logic import And, InClass
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = VecSpaces(K)
expr = And(ExprRange(sub_expr1, InClass(IndexedVar(U, sub_expr1), sub_expr2), one, i), InClass(V, sub_expr2), ExprRange(sub_expr1, InClass(IndexedVar(W, sub_expr1), sub_expr2), one, k))

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(U_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \left(U_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \ldots \land  \left(U_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land \left(V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\land \left(W_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \left(W_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \ldots \land  \left(W_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	ExprRange	lambda_map: 6 start_index: 10 end_index: 7
4	Operation	operator: 16 operands: 8
5	ExprRange	lambda_map: 9 start_index: 10 end_index: 11
6	Lambda	parameter: 26 body: 12
7	Variable
8	ExprTuple	13, 20
9	Lambda	parameter: 26 body: 14
10	Literal
11	Variable
12	Operation	operator: 16 operands: 15
13	Variable
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 20
16	Literal
17	ExprTuple	19, 20
18	IndexedVar	variable: 21 index: 26
19	IndexedVar	variable: 22 index: 26
20	Operation	operator: 24 operand: 27
21	Variable
22	Variable
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Variable
27	Variable