Expression of type Forall

from the theory of proveit.linear_algebra

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, S, T, V, W, v
from proveit.linear_algebra import LinMap, LinMapAdd
from proveit.logic import Equals, Forall
from proveit.numbers import Add

# build up the expression from sub-expressions
sub_expr1 = [v]
expr = Forall(instance_param_or_params = [V, W], instance_expr = Forall(instance_param_or_params = [S, T], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(LinMapAdd(S, T), sub_expr1), Add(Function(S, sub_expr1), Function(T, sub_expr1))), 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_{V, W}~\left[\forall_{S, T \in \mathcal{L}\left(V, W\right)}~\left[\forall_{v \in V}~\left(\left(S + T\right)\left(v\right) = \left(S\left(v\right) + T\left(v\right)\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: 9 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 27 body: 3
3	Operation	operator: 9 operand: 5
4	ExprTuple	5
5	Lambda	parameters: 36 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15
13	Lambda	parameter: 42 body: 16
14	Operation	operator: 24 operands: 17
15	Operation	operator: 24 operands: 18
16	Conditional	value: 19 condition: 20
17	ExprTuple	39, 21
18	ExprTuple	40, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	42, 30
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operand: 42
29	Operation	operator: 33 operands: 34
30	Variable
31	Variable
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39, 40
37	Operation	operator: 39 operand: 42
38	Operation	operator: 40 operand: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable