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, b, x, y
from proveit.linear_algebra import VecSpaces, binary_lin_comb_ax_by
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, b], instance_expr = Forall(instance_param_or_params = [x, y], instance_expr = InSet(binary_lin_comb_ax_by, 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, b \in K}~\left[\forall_{x, y \in V}~\left(\left(\left(a \cdot x\right) + \left(b \cdot y\right)\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: 33 body: 3
3	Operation	operator: 21 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 47 body: 7
6	ExprTuple	47
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	47, 14
13	Lambda	parameters: 15 body: 16
14	Operation	operator: 17 operand: 33
15	ExprTuple	51, 53
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	33
19	Operation	operator: 21 operand: 24
20	Operation	operator: 35 operands: 23
21	Literal
22	ExprTuple	24
23	ExprTuple	25, 26
24	Lambda	parameters: 27 body: 28
25	Operation	operator: 43 operands: 29
26	Operation	operator: 43 operands: 30
27	ExprTuple	52, 54
28	Conditional	value: 31 condition: 32
29	ExprTuple	51, 33
30	ExprTuple	53, 33
31	Operation	operator: 43 operands: 34
32	Operation	operator: 35 operands: 36
33	Variable
34	ExprTuple	37, 47
35	Literal
36	ExprTuple	38, 39
37	Operation	operator: 40 operands: 41
38	Operation	operator: 43 operands: 42
39	Operation	operator: 43 operands: 44
40	Literal
41	ExprTuple	45, 46
42	ExprTuple	52, 47
43	Literal
44	ExprTuple	54, 47
45	Operation	operator: 49 operands: 48
46	Operation	operator: 49 operands: 50
47	Variable
48	ExprTuple	51, 52
49	Literal
50	ExprTuple	53, 54
51	Variable
52	Variable
53	Variable
54	Variable