Expression of type Lambda

from the theory of proveit.linear_algebra.inner_products

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, P, X
from proveit.linear_algebra import Hspace, OrthoProj
from proveit.logic import Equals, Forall, SubsetEq
from proveit.numbers import Exp, two

# build up the expression from sub-expressions
expr = Lambda(X, Conditional(Forall(instance_param_or_params = [P], instance_expr = Equals(Exp(P, two), P), condition = Equals(P, OrthoProj(Hspace, X))), SubsetEq(X, Hspace)))

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())

X \mapsto \left\{\forall_{P~|~P = \textrm{OrthoProj}\left(\mathcal{H}, X\right)}~\left(P^{2} = P\right) \textrm{ if } X \subseteq \mathcal{H}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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