Expression of type Lambda

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, Lambda, 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 = Lambda([m, n], 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(m, n\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	29, 30
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: 28 body: 13
10	Operation	operator: 20 operands: 14
11	Operation	operator: 20 operands: 15
12	ExprTuple	28
13	Conditional	value: 16 condition: 17
14	ExprTuple	29, 18
15	ExprTuple	30, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	28, 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operand: 30
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30
28	Variable
29	Variable
30	Variable