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Expression of type Forall

from the theory of proveit.linear_algebra.scalar_multiplication

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 V
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import lin_comb_axn
from proveit.logic import Forall, InSet
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(lin_comb_axn, V), domain = V)
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_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) \in V\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple6
5Conditionalvalue: 7
condition: 8
6ExprRangelambda_map: 9
start_index: 21
end_index: 22
7Operationoperator: 23
operands: 10
8Operationoperator: 11
operands: 12
9Lambdaparameter: 34
body: 30
10ExprTuple13, 26
11Literal
12ExprTuple14
13Operationoperator: 15
operands: 16
14ExprRangelambda_map: 17
start_index: 21
end_index: 22
15Literal
16ExprTuple18
17Lambdaparameter: 34
body: 19
18ExprRangelambda_map: 20
start_index: 21
end_index: 22
19Operationoperator: 23
operands: 24
20Lambdaparameter: 34
body: 25
21Literal
22Variable
23Literal
24ExprTuple30, 26
25Operationoperator: 27
operands: 28
26Variable
27Literal
28ExprTuple29, 30
29IndexedVarvariable: 31
index: 34
30IndexedVarvariable: 32
index: 34
31Variable
32Variable
33ExprTuple34
34Variable