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 Conditional, Lambda, M, m, n, x
from proveit.linear_algebra import MatrixMult, MatrixSpace
from proveit.logic import CartExp, Equals, Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [M], instance_expr = Equals(Qmult(M), Lambda(x, Conditional(MatrixMult(M, x), InSet(x, CartExp(Complex, n))))), domain = MatrixSpace(field = Complex, rows = m, columns = n))

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_{M \in \mathbb{C}^{m \times n}}~\left(\left[M\right] = \left[x \mapsto \left\{M \thinspace x \textrm{ if } x \in \mathbb{C}^{n}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 26 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 24 operands: 9
7	Literal
8	ExprTuple	10, 11
9	ExprTuple	26, 12
10	Operation	operator: 13 operand: 26
11	Lambda	parameter: 27 body: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	26
15	ExprTuple	27
16	Conditional	value: 19 condition: 20
17	Literal
18	NamedExprs	field: 31 rows: 21 columns: 32
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Variable
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Variable