Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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