Expression of type Forall

from the theory of proveit.physics.quantum.algebra

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 X, c
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [c], instance_expr = Forall(instance_param_or_params = [X], instance_expr = Equals(Qmult(c, X), ScalarMult(c, X)), domain = QmultCodomain), domain = Complex)

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_{c \in \mathbb{C}}~\left[\forall_{X \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\left(c \thinspace X\right) = \left(c \cdot X\right)\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: 27 body: 4
3	ExprTuple	27
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	27, 12
11	Lambda	parameter: 28 body: 14
12	Literal
13	ExprTuple	28
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	28, 23
21	Operation	operator: 24 operands: 26
22	Operation	operator: 25 operands: 26
23	Literal
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Variable