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 ExprRange, Function, IndexedVar, Q, Variable, c, f, j, m, n
from proveit.linear_algebra import MatrixSpace
from proveit.logic import Forall, InSet
from proveit.numbers import Complex, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, j)]
expr = Forall(instance_param_or_params = sub_expr2, instance_expr = InSet(Function(f, sub_expr2), MatrixSpace(field = Complex, rows = n, columns = m)), condition = Function(Q, sub_expr2))

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_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~\left(f\left(c_{1}, c_{2}, \ldots, c_{j}\right) \in \mathbb{C}^{n \times m}\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: 13 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 13
7	Literal
8	ExprTuple	10, 11
9	Variable
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Variable
13	ExprTuple	16
14	Literal
15	NamedExprs	field: 17 rows: 18 columns: 19
16	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
17	Literal
18	Variable
19	Variable
20	Lambda	parameter: 26 body: 23
21	Literal
22	Variable
23	IndexedVar	variable: 24 index: 26
24	Variable
25	ExprTuple	26
26	Variable