# 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.
# import Expression classes needed to build the expression
from proveit import A, B, Conditional, Function, Lambda, V, W, x
from proveit.logic import Equals, Forall, InSet

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Forall(instance_param_or_params = [V, W], instance_expr = Forall(instance_param_or_params = [A, B], instance_expr = Equals(VecAdd(A, B), Lambda(x, Conditional(VecAdd(Function(A, sub_expr1), Function(B, sub_expr1)), InSet(x, V)))), domain = LinMap(V, W)))

Out[2]:
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, W}~\left[\forall_{A, B \in \mathcal{L}\left(V, W\right)}~\left(\left(A + B\right) = \left[x \mapsto \left\{A\left(x\right) + B\left(x\right) \textrm{ if } x \in V\right..\right]\right)\right]

In [5]:
stored_expr.style_options()

Out[5]:
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()

Out[6]:
core typesub-expressionsexpression
0Operationoperator: 4
operand: 2
1ExprTuple2
2Lambdaparameters: 30
body: 3
3Operationoperator: 4
operand: 6
4Literal
5ExprTuple6
6Lambdaparameters: 18
body: 7
7Conditionalvalue: 8
condition: 9
8Operationoperator: 10
operands: 11
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14, 15
12Literal
13ExprTuple16, 17
14Operationoperator: 25
operands: 18
15Lambdaparameter: 38
body: 19
16Operationoperator: 27
operands: 20
17Operationoperator: 27
operands: 21
18ExprTuple35, 36
19Conditionalvalue: 22
condition: 23
20ExprTuple35, 24
21ExprTuple36, 24
22Operationoperator: 25
operands: 26
23Operationoperator: 27
operands: 28
24Operationoperator: 29
operands: 30
25Literal
26ExprTuple31, 32
27Literal
28ExprTuple38, 33
29Literal
30ExprTuple33, 34
31Operationoperator: 35
operand: 38
32Operationoperator: 36
operand: 38
33Variable
34Variable
35Variable
36Variable
37ExprTuple38
38Variable