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Expression of type Forall

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.core_expr_types import V_1_to_i, a_1_to_i
from proveit.linear_algebra import TensorProd
from proveit.logic import Forall, InSet
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(TensorProd(a_1_to_i), TensorProd(V_1_to_i)), domains = [V_1_to_i])
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())
\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)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 13
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 24
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple12
10Operationoperator: 14
operands: 13
11Operationoperator: 14
operands: 15
12ExprRangelambda_map: 16
start_index: 22
end_index: 23
13ExprTuple17
14Literal
15ExprTuple18
16Lambdaparameter: 31
body: 19
17ExprRangelambda_map: 20
start_index: 22
end_index: 23
18ExprRangelambda_map: 21
start_index: 22
end_index: 23
19Operationoperator: 24
operands: 25
20Lambdaparameter: 31
body: 26
21Lambdaparameter: 31
body: 27
22Literal
23Variable
24Literal
25ExprTuple26, 27
26IndexedVarvariable: 28
index: 31
27IndexedVarvariable: 29
index: 31
28Variable
29Variable
30ExprTuple31
31Variable