Expression of type Forall

from the theory of proveit.linear_algebra.linear_maps

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 K, V, W
from proveit.linear_algebra import LinMap, VecSpaces
from proveit.logic import Forall, InClass

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = Forall(instance_param_or_params = [K], instance_expr = Forall(instance_param_or_params = [V, W], instance_expr = InClass(LinMap(V, W), sub_expr1), domain = sub_expr1))

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())

\forall_{K}~\left[\forall_{V, W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(\mathcal{L}\left(V, W\right) \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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