Expression of type Forall

from the theory of proveit.linear_algebra.scalar_multiplication

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, a, x
from proveit.linear_algebra import ScalarMult, VecSpaces
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [K], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [a], instance_expr = Forall(instance_param_or_params = [x], instance_expr = InSet(ScalarMult(a, x), V), domain = V), domain = K), domain = VecSpaces(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())

\forall_{K}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{a \in K}~\left[\forall_{x \in V}~\left(\left(a \cdot x\right) \in V\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: 21 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 25 body: 3
3	Operation	operator: 21 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 34 body: 7
6	ExprTuple	34
7	Conditional	value: 8 condition: 9
8	Operation	operator: 21 operand: 13
9	Operation	operator: 11 operands: 12
10	ExprTuple	13
11	Literal
12	ExprTuple	34, 14
13	Lambda	parameter: 37 body: 16
14	Operation	operator: 17 operand: 25
15	ExprTuple	37
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	25
19	Operation	operator: 21 operand: 24
20	Operation	operator: 31 operands: 23
21	Literal
22	ExprTuple	24
23	ExprTuple	37, 25
24	Lambda	parameter: 38 body: 27
25	Variable
26	ExprTuple	38
27	Conditional	value: 28 condition: 29
28	Operation	operator: 31 operands: 30
29	Operation	operator: 31 operands: 32
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	38, 34
33	Operation	operator: 35 operands: 36
34	Variable
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Variable