Expression of type Lambda

from the theory of proveit.linear_algebra.matrices

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, n
from proveit.linear_algebra import MatrixSpace, Unitary
from proveit.logic import InSet, SubsetEq
from proveit.numbers import Complex, NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(SubsetEq(Unitary(n), MatrixSpace(field = Complex, rows = n, columns = n)), 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())

n \mapsto \left\{\textrm{U}\left(n\right) \subseteq \mathbb{C}^{n \times n} \textrm{ if } 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	parameter: 16 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	16, 10
8	Operation	operator: 11 operand: 16
9	Operation	operator: 13 operands: 14
10	Literal
11	Literal
12	ExprTuple	16
13	Literal
14	NamedExprs	field: 15 rows: 16 columns: 16
15	Literal
16	Variable