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

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

K \mapsto \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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 19 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 37 body: 5
4	ExprTuple	37
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	37, 13
12	Lambda	parameters: 39 body: 14
13	Operation	operator: 15 operand: 19
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Variable
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 41 operand: 34
25	Operation	operator: 29 operands: 30
26	Operation	operator: 32 operands: 31
27	Operation	operator: 32 operands: 33
28	ExprTuple	34
29	Literal
30	ExprTuple	35, 36
31	ExprTuple	43, 37
32	Literal
33	ExprTuple	44, 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 41 operand: 43
36	Operation	operator: 41 operand: 44
37	Variable
38	Literal
39	ExprTuple	43, 44
40	ExprTuple	43
41	Literal
42	ExprTuple	44
43	Variable
44	Variable