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, U, Variable, W, a, c, d, f, i, k
from proveit.logic import And, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(U, sub_expr1)
sub_expr3 = IndexedVar(W, sub_expr1)
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), sub_expr3), one, k), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InSet(IndexedVar(f, sub_expr1), sub_expr3), 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(a_{1} \in U_{1}\right) \land  \left(a_{2} \in U_{2}\right) \land  \ldots \land  \left(a_{i} \in U_{i}\right)\land \left(c_{1} \in W_{1}\right) \land  \left(c_{2} \in W_{2}\right) \land  \ldots \land  \left(c_{k} \in W_{k}\right)\land \left(d_{1} \in U_{1}\right) \land  \left(d_{2} \in U_{2}\right) \land  \ldots \land  \left(d_{i} \in U_{i}\right)\land \left(f_{1} \in W_{1}\right) \land  \left(f_{2} \in W_{2}\right) \land  \ldots \land  \left(f_{k} \in W_{k}\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, 6
3	ExprRange	lambda_map: 7 start_index: 12 end_index: 10
4	ExprRange	lambda_map: 8 start_index: 12 end_index: 13
5	ExprRange	lambda_map: 9 start_index: 12 end_index: 10
6	ExprRange	lambda_map: 11 start_index: 12 end_index: 13
7	Lambda	parameter: 36 body: 14
8	Lambda	parameter: 36 body: 15
9	Lambda	parameter: 36 body: 16
10	Variable
11	Lambda	parameter: 36 body: 17
12	Literal
13	Variable
14	Operation	operator: 21 operands: 18
15	Operation	operator: 21 operands: 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	23, 26
19	ExprTuple	24, 28
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	27, 28
23	IndexedVar	variable: 29 index: 36
24	IndexedVar	variable: 30 index: 36
25	IndexedVar	variable: 31 index: 36
26	IndexedVar	variable: 32 index: 36
27	IndexedVar	variable: 33 index: 36
28	IndexedVar	variable: 34 index: 36
29	Variable
30	Variable
31	Variable
32	Variable
33	Variable
34	Variable
35	ExprTuple	36
36	Variable