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Expression of type Conditional

from the theory of proveit.linear_algebra

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 Conditional, Function, S, T, V, W, v
from proveit.linear_algebra import LinMap, LinMapAdd
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [v]
sub_expr2 = LinMap(V, W)
expr = Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(LinMapAdd(S, T), sub_expr1), Add(Function(S, sub_expr1), Function(T, sub_expr1))), domain = V), And(InSet(S, sub_expr2), InSet(T, sub_expr2)))
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_{v \in V}~\left(\left(S + T\right)\left(v\right) = \left(S\left(v\right) + T\left(v\right)\right)\right) \textrm{ if } S \in \mathcal{L}\left(V, W\right) ,  T \in \mathcal{L}\left(V, W\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
6ExprTuple8, 9
7Lambdaparameter: 36
body: 10
8Operationoperator: 18
operands: 11
9Operationoperator: 18
operands: 12
10Conditionalvalue: 13
condition: 14
11ExprTuple33, 15
12ExprTuple34, 15
13Operationoperator: 16
operands: 17
14Operationoperator: 18
operands: 19
15Operationoperator: 20
operands: 21
16Literal
17ExprTuple22, 23
18Literal
19ExprTuple36, 24
20Literal
21ExprTuple24, 25
22Operationoperator: 26
operand: 36
23Operationoperator: 27
operands: 28
24Variable
25Variable
26Operationoperator: 29
operands: 30
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple33, 34
31Operationoperator: 33
operand: 36
32Operationoperator: 34
operand: 36
33Variable
34Variable
35ExprTuple36
36Variable