Expression of type Lambda

from the theory of proveit.linear_algebra.inner_products

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, H, Lambda, x, y
from proveit.linear_algebra import Norm, VecAdd
from proveit.logic import And, InSet
from proveit.numbers import Add, LessEq

# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(LessEq(Norm(VecAdd(x, y)), Add(Norm(x), Norm(y))), And(InSet(x, H), InSet(y, H))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(x, y\right) \mapsto \left\{\left \|x + y\right \| \leq \left(\left \|x\right \| + \left \|y\right \|\right) \textrm{ if } x \in H ,  y \in H\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 23 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 25 operand: 18
9	Operation	operator: 13 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18
13	Literal
14	ExprTuple	19, 20
15	ExprTuple	27, 21
16	Literal
17	ExprTuple	28, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 25 operand: 27
20	Operation	operator: 25 operand: 28
21	Variable
22	Literal
23	ExprTuple	27, 28
24	ExprTuple	27
25	Literal
26	ExprTuple	28
27	Variable
28	Variable