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 Function, P, Px, V, W, x, y
from proveit.linear_algebra import LinMap, VecAdd
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [P], instance_expr = Forall(instance_param_or_params = [x, y], instance_expr = Equals(Function(P, [VecAdd(x, y)]), VecAdd(Px, Function(P, [y]))), domain = V), domain = LinMap(V, W))

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_{P \in \mathcal{L}\left(V, W\right)}~\left[\forall_{x, y \in V}~\left(P\left(x + y\right) = \left(P\left(x\right) + P\left(y\right)\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 38 body: 4
3	ExprTuple	38
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 29 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	38, 11
10	Lambda	parameters: 36 body: 12
11	Operation	operator: 13 operands: 14
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	34, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 38 operand: 31
23	Operation	operator: 35 operands: 27
24	Operation	operator: 29 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprTuple	31
27	ExprTuple	32, 33
28	ExprTuple	40, 34
29	Literal
30	ExprTuple	41, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 38 operand: 40
33	Operation	operator: 38 operand: 41
34	Variable
35	Literal
36	ExprTuple	40, 41
37	ExprTuple	40
38	Variable
39	ExprTuple	41
40	Variable
41	Variable