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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 A, B, C, ExprRange, IndexedVar, K, Variable, i, j, k
from proveit.linear_algebra import VecSpaces
from proveit.logic import And, InClass
from proveit.numbers import one
In [2]:
# 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(A, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InClass(IndexedVar(B, sub_expr1), sub_expr2), one, j), ExprRange(sub_expr1, InClass(IndexedVar(C, sub_expr1), sub_expr2), 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} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \left(A_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \ldots \land  \left(A_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\land \left(B_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \left(B_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \ldots \land  \left(B_{j} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\land \left(C_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \left(C_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \ldots \land  \left(C_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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
3ExprRangelambda_map: 6
start_index: 11
end_index: 7
4ExprRangelambda_map: 8
start_index: 11
end_index: 9
5ExprRangelambda_map: 10
start_index: 11
end_index: 12
6Lambdaparameter: 30
body: 13
7Variable
8Lambdaparameter: 30
body: 14
9Variable
10Lambdaparameter: 30
body: 15
11Literal
12Variable
13Operationoperator: 18
operands: 16
14Operationoperator: 18
operands: 17
15Operationoperator: 18
operands: 19
16ExprTuple20, 23
17ExprTuple21, 23
18Literal
19ExprTuple22, 23
20IndexedVarvariable: 24
index: 30
21IndexedVarvariable: 25
index: 30
22IndexedVarvariable: 26
index: 30
23Operationoperator: 28
operand: 31
24Variable
25Variable
26Variable
27ExprTuple30
28Literal
29ExprTuple31
30Variable
31Variable