Expression of type Conditional

from the theory of proveit.linear_algebra.matrices.exponentiation

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 A, Conditional, m, n
from proveit.linear_algebra import MatrixExp, Unitary
from proveit.logic import And, Forall, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Unitary(n)
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = InSet(MatrixExp(A, m), sub_expr1), domain = sub_expr1), 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\{\forall_{A \in \textrm{U}\left(n\right)}~\left(A^{m} \in \textrm{U}\left(n\right)\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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