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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 Conditional, Lambda, P, Px, V, W, c, x
from proveit.linear_algebra import LinMap, ScalarMult
from proveit.logic import Equals, Forall, InSet
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [V, W], instance_expr = Forall(instance_param_or_params = [c, P], instance_expr = Equals(ScalarMult(c, P), Lambda(x, Conditional(ScalarMult(c, Px), 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_{c, P \in \mathcal{L}\left(V, W\right)}~\left(\left(c \cdot P\right) = \left[x \mapsto \left\{c \cdot P\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: 37
body: 19
16Operationoperator: 27
operands: 20
17Operationoperator: 27
operands: 21
18ExprTuple31, 35
19Conditionalvalue: 22
condition: 23
20ExprTuple31, 24
21ExprTuple35, 24
22Operationoperator: 25
operands: 26
23Operationoperator: 27
operands: 28
24Operationoperator: 29
operands: 30
25Literal
26ExprTuple31, 32
27Literal
28ExprTuple37, 33
29Literal
30ExprTuple33, 34
31Variable
32Operationoperator: 35
operand: 37
33Variable
34Variable
35Variable
36ExprTuple37
37Variable