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 binary_lin_comb_ax_by
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
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)

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_{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]

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	parameters: 3 body: 4
3	ExprTuple	37, 39
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 21 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 13 body: 14
11	Operation	operator: 29 operands: 15
12	Operation	operator: 29 operands: 16
13	ExprTuple	38, 40
14	Conditional	value: 17 condition: 18
15	ExprTuple	37, 19
16	ExprTuple	39, 19
17	Operation	operator: 29 operands: 20
18	Operation	operator: 21 operands: 22
19	Variable
20	ExprTuple	23, 33
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 29 operands: 28
25	Operation	operator: 29 operands: 30
26	Literal
27	ExprTuple	31, 32
28	ExprTuple	38, 33
29	Literal
30	ExprTuple	40, 33
31	Operation	operator: 35 operands: 34
32	Operation	operator: 35 operands: 36
33	Variable
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39, 40
37	Variable
38	Variable
39	Variable
40	Variable