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In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.linear_algebra.inner_products import scaled_norm
In [2]:
# check that the built expression is the same as the stored expression
assert scaled_norm.expr == stored_expr
assert scaled_norm.expr._style_id == stored_expr._style_id
print("Passed sanity check: scaled_norm matches stored_expr")
Passed sanity check: scaled_norm matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{K}~\left[\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\left[\forall_{\alpha \in K, x \in H}~\left(\left \|\alpha \cdot x\right \| = \left(\left|\alpha\right| \cdot \left \|x\right \|\right)\right)\right]\right]
In [4]:
stored_expr.style_options()
Out[4]:
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 [5]:
# display the expression information
stored_expr.expr_info()
Out[5]:
 core typesub-expressionsexpression
0Operationoperator: 10
operand: 2
1ExprTuple2
2Lambdaparameter: 38
body: 3
3Operationoperator: 10
operand: 5
4ExprTuple5
5Lambdaparameter: 39
body: 7
6ExprTuple39
7Conditionalvalue: 8
condition: 9
8Operationoperator: 10
operand: 14
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14
12Literal
13ExprTuple39, 15
14Lambdaparameters: 41
body: 16
15Operationoperator: 17
operand: 38
16Conditionalvalue: 19
condition: 20
17Literal
18ExprTuple38
19Operationoperator: 21
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple25, 26
23Literal
24ExprTuple27, 28
25Operationoperator: 44
operand: 35
26Operationoperator: 30
operands: 31
27Operationoperator: 33
operands: 32
28Operationoperator: 33
operands: 34
29ExprTuple35
30Literal
31ExprTuple36, 37
32ExprTuple46, 38
33Literal
34ExprTuple47, 39
35Operationoperator: 40
operands: 41
36Operationoperator: 42
operand: 46
37Operationoperator: 44
operand: 47
38Variable
39Variable
40Literal
41ExprTuple46, 47
42Literal
43ExprTuple46
44Literal
45ExprTuple47
46Variable
47Variable