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 H, K, Lambda
from proveit.linear_algebra import InnerProdSpaces, VecSpaces
from proveit.logic import Forall, InClass

# build up the expression from sub-expressions
expr = Lambda(K, Forall(instance_param_or_params = [H], instance_expr = InClass(H, VecSpaces(K)), domain = InnerProdSpaces(K)))

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())

K \mapsto \left[\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\left(H \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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