# from the theory of proveit.linear_algebra.inner_products¶

see dependencies

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.
# import the special expression
from proveit.linear_algebra.inner_products import norm_triangle_ineq

In [2]:
# check that the built expression is the same as the stored expression
assert norm_triangle_ineq.expr == stored_expr
assert norm_triangle_ineq.expr._style_id == stored_expr._style_id
print("Passed sanity check: norm_triangle_ineq matches stored_expr")

Passed sanity check: norm_triangle_ineq 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_{x, y \in H}~\left(\left \|x + y\right \| \leq \left(\left \|x\right \| + \left \|y\right \|\right)\right)\right]\right]

In [4]:
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 [5]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 10
operand: 2
1ExprTuple2
2Lambdaparameter: 21
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: 21
16Conditionalvalue: 19
condition: 20
17Literal
18ExprTuple21
19Operationoperator: 22
operands: 23
20Operationoperator: 24
operands: 25
21Variable
22Literal
23ExprTuple26, 27
24Literal
25ExprTuple28, 29
26Operationoperator: 43
operand: 36
27Operationoperator: 31
operands: 32
28Operationoperator: 34
operands: 33
29Operationoperator: 34
operands: 35
30ExprTuple36
31Literal
32ExprTuple37, 38
33ExprTuple45, 39
34Literal
35ExprTuple46, 39
36Operationoperator: 40
operands: 41
37Operationoperator: 43
operand: 45
38Operationoperator: 43
operand: 46
39Variable
40Literal
41ExprTuple45, 46
42ExprTuple45
43Literal
44ExprTuple46
45Variable
46Variable