Expression of type Forall

from the theory of proveit.logic.sets.unification

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 S
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Forall, SubsetEq, Union
from proveit.logic.sets import each_A_in_S

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A_1_to_m, S], instance_expr = SubsetEq(Union(A_1_to_m), S), condition = each_A_in_S)

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_{1}, A_{2}, \ldots, A_{m}, S~|~\left(A_{1} \subseteq S\right), \left(A_{2} \subseteq S\right), \ldots, \left(A_{m} \subseteq S\right)}~\left(\left(A_{1} \cup  A_{2} \cup  \ldots \cup  A_{m}\right) \subseteq S\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	16, 24
5	Conditional	value: 6 condition: 7
6	Operation	operator: 21 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 24
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operands: 14
12	ExprRange	lambda_map: 15 start_index: 19 end_index: 20
13	Literal
14	ExprTuple	16
15	Lambda	parameter: 27 body: 17
16	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
17	Operation	operator: 21 operands: 22
18	Lambda	parameter: 27 body: 23
19	Literal
20	Variable
21	Literal
22	ExprTuple	23, 24
23	IndexedVar	variable: 25 index: 27
24	Variable
25	Variable
26	ExprTuple	27
27	Variable