Expression of type Forall

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, x
from proveit.linear_algebra import InnerProdSpaces, Norm
from proveit.logic import Forall, InSet
from proveit.numbers import RealNonNeg

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [H], instance_expr = Forall(instance_param_or_params = [x], instance_expr = InSet(Norm(x), RealNonNeg), domain = H), domain = InnerProdSpaces(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())

\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(H\right)}~\left[\forall_{x \in H}~\left(\left \|x\right \| \in \mathbb{R}^{\ge 0}\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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