Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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