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Expression of type And

from the theory of proveit.linear_algebra.tensors

In [1]:
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, e, i, k
from proveit.logic import And, InSet
from proveit.numbers import one
In [2]:
# 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(e, sub_expr1), sub_expr3), one, k))
expr:
In [3]:
# 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
In [4]:
# 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(e_{1} \in W_{1}\right) \land  \left(e_{2} \in W_{2}\right) \land  \ldots \land  \left(e_{k} \in W_{k}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4, 5, 6
3ExprRangelambda_map: 7
start_index: 12
end_index: 10
4ExprRangelambda_map: 8
start_index: 12
end_index: 13
5ExprRangelambda_map: 9
start_index: 12
end_index: 10
6ExprRangelambda_map: 11
start_index: 12
end_index: 13
7Lambdaparameter: 36
body: 14
8Lambdaparameter: 36
body: 15
9Lambdaparameter: 36
body: 16
10Variable
11Lambdaparameter: 36
body: 17
12Literal
13Variable
14Operationoperator: 21
operands: 18
15Operationoperator: 21
operands: 19
16Operationoperator: 21
operands: 20
17Operationoperator: 21
operands: 22
18ExprTuple23, 26
19ExprTuple24, 28
20ExprTuple25, 26
21Literal
22ExprTuple27, 28
23IndexedVarvariable: 29
index: 36
24IndexedVarvariable: 30
index: 36
25IndexedVarvariable: 31
index: 36
26IndexedVarvariable: 32
index: 36
27IndexedVarvariable: 33
index: 36
28IndexedVarvariable: 34
index: 36
29Variable
30Variable
31Variable
32Variable
33Variable
34Variable
35ExprTuple36
36Variable