Expression of type Forall

from the theory of proveit.physics.quantum

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 alpha, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import QubitSpace

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x], instance_expr = Forall(instance_param_or_params = [alpha], instance_expr = InSet(ScalarMult(alpha, x), QubitSpace), domain = Complex), domain = QubitSpace)

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_{x \in \mathbb{C}^{2}}~\left[\forall_{\alpha \in \mathbb{C}}~\left(\left(\alpha \cdot x\right) \in \mathbb{C}^{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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 25 body: 4
3	ExprTuple	25
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 16 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	25, 19
10	Lambda	parameter: 24 body: 12
11	ExprTuple	24
12	Conditional	value: 13 condition: 14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	24, 26
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Variable
25	Variable
26	Literal
27	Literal