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Expression of type Conditional

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, Conditional, K, V
from proveit.linear_algebra import Commutator, VecAdd, VecNeg, VecSpaces
from proveit.logic import Equals, Forall, InClass
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A, B], instance_expr = Equals(Commutator(A, B), VecAdd(Composition(A, B), VecNeg(Composition(B, A)))), domain = V), InClass(V, 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())
\left\{\forall_{A, B \in V}~\left(\left[A, B\right] = \left(\left(A \circ B\right) + \left(-\left(B \circ A\right)\right)\right)\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple31, 8
7Lambdaparameters: 32
body: 9
8Operationoperator: 10
operand: 14
9Conditionalvalue: 12
condition: 13
10Literal
11ExprTuple14
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operands: 18
14Variable
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple21, 22
19Operationoperator: 23
operands: 32
20Operationoperator: 24
operands: 25
21Operationoperator: 27
operands: 26
22Operationoperator: 27
operands: 28
23Literal
24Literal
25ExprTuple29, 30
26ExprTuple39, 31
27Literal
28ExprTuple38, 31
29Operationoperator: 36
operands: 32
30Operationoperator: 33
operand: 35
31Variable
32ExprTuple39, 38
33Literal
34ExprTuple35
35Operationoperator: 36
operands: 37
36Literal
37ExprTuple38, 39
38Variable
39Variable