Expression of type And

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, x, y
from proveit.linear_algebra import InnerProd, VecSpaces
from proveit.logic import And, Forall, InClass, InSet

# build up the expression from sub-expressions
expr = And(InClass(H, VecSpaces(K)), Forall(instance_param_or_params = [x, y], instance_expr = InSet(InnerProd(x, y), 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())

\left(H \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land \left[\forall_{x, y}~\left(\left \langle x, y\right \rangle \in K\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operand: 11
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11
9	Variable
10	Operation	operator: 12 operand: 18
11	Lambda	parameters: 20 body: 14
12	Literal
13	ExprTuple	18
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 19 operands: 20
18	Variable
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Variable