Expression of type Lambda

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
from proveit.linear_algebra import MatrixSpace
from proveit.logic import And, Forall, InClass, InSet
from proveit.numbers import Complex, NaturalPos
from proveit.physics.quantum import Qmult, QmultCodomain

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

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())

\left(m, n\right) \mapsto \left\{\forall_{M \in \mathbb{C}^{m \times n}}~\left(\left[M\right] \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	31, 32
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 29 body: 12
10	Operation	operator: 20 operands: 13
11	Operation	operator: 20 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	31, 17
14	ExprTuple	32, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	29, 24
22	Operation	operator: 25 operand: 29
23	Literal
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29
27	Literal
28	NamedExprs	field: 30 rows: 31 columns: 32
29	Variable
30	Literal
31	Variable
32	Variable