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Expression of type Forall

from the theory of proveit.linear_algebra.linear_maps

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, Composition, K, V
from proveit.linear_algebra import AntiCommutator, VecAdd, VecSpaces
from proveit.logic import Equals, Forall
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [A, B], instance_expr = Equals(AntiCommutator(A, B), VecAdd(Composition(A, B), Composition(B, A))), domain = V), domain = VecSpaces(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())
\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{A, B \in V}~\left(\left\{A, B\right\} = \left(\left(A \circ B\right) + \left(B \circ A\right)\right)\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: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 35
body: 4
3ExprTuple35
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple35, 12
11Lambdaparameters: 36
body: 13
12Operationoperator: 14
operand: 18
13Conditionalvalue: 16
condition: 17
14Literal
15ExprTuple18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Variable
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple25, 26
23Operationoperator: 27
operands: 36
24Operationoperator: 28
operands: 29
25Operationoperator: 31
operands: 30
26Operationoperator: 31
operands: 32
27Literal
28Literal
29ExprTuple33, 34
30ExprTuple40, 35
31Literal
32ExprTuple39, 35
33Operationoperator: 37
operands: 36
34Operationoperator: 37
operands: 38
35Variable
36ExprTuple40, 39
37Literal
38ExprTuple39, 40
39Variable
40Variable