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, K, Lambda, x, y
from proveit.linear_algebra import InnerProdSpaces, Norm, VecAdd
from proveit.logic import Forall, InClass
from proveit.numbers import Add, LessEq

# build up the expression from sub-expressions
expr = Lambda(H, Conditional(Forall(instance_param_or_params = [x, y], instance_expr = LessEq(Norm(VecAdd(x, y)), Add(Norm(x), Norm(y))), domain = H), InClass(H, InnerProdSpaces(K))))

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())

H \mapsto \left\{\forall_{x, y \in H}~\left(\left \|x + y\right \| \leq \left(\left \|x\right \| + \left \|y\right \|\right)\right) \textrm{ if } H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 34 body: 2
1	ExprTuple	34
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	34, 10
9	Lambda	parameters: 36 body: 11
10	Operation	operator: 12 operand: 16
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Variable
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 38 operand: 31
22	Operation	operator: 26 operands: 27
23	Operation	operator: 29 operands: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	31
26	Literal
27	ExprTuple	32, 33
28	ExprTuple	40, 34
29	Literal
30	ExprTuple	41, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 38 operand: 40
33	Operation	operator: 38 operand: 41
34	Variable
35	Literal
36	ExprTuple	40, 41
37	ExprTuple	40
38	Literal
39	ExprTuple	41
40	Variable
41	Variable