Expression of type Forall

from the theory of proveit.linear_algebra.addition

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 V, a, b
from proveit.linear_algebra import InnerProd, Norm, VecAdd
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Exp, sqrt, two, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = Equals(Norm(VecAdd(a, b)), sqrt(Add(Exp(Norm(a), two), Exp(Norm(b), two)))), domain = V, condition = Equals(InnerProd(a, b), zero))

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_{a, b \in V~|~\left \langle a, b\right \rangle = 0}~\left(\left \|a + b\right \| = \sqrt{\left(\left \|a\right \|^{2} + \left \|b\right \|^{2}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 34 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 20 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 45 operand: 22
11	Operation	operator: 39 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	Operation	operator: 20 operands: 21
15	ExprTuple	22
16	ExprTuple	23, 24
17	ExprTuple	47, 25
18	Literal
19	ExprTuple	48, 25
20	Literal
21	ExprTuple	26, 27
22	Operation	operator: 28 operands: 34
23	Operation	operator: 29 operands: 30
24	Operation	operator: 31 operands: 32
25	Variable
26	Operation	operator: 33 operands: 34
27	Literal
28	Literal
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	37, 43
33	Literal
34	ExprTuple	47, 48
35	Operation	operator: 39 operands: 38
36	Operation	operator: 39 operands: 40
37	Literal
38	ExprTuple	41, 43
39	Literal
40	ExprTuple	42, 43
41	Operation	operator: 45 operand: 47
42	Operation	operator: 45 operand: 48
43	Literal
44	ExprTuple	47
45	Literal
46	ExprTuple	48
47	Variable
48	Variable