Expression of type Conditional

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 Conditional, S, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Forall, InSet, SubsetEq, Union
from proveit.logic.sets import each_A_in_S
from proveit.numbers import NaturalPos

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

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())

\left\{\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) \textrm{ if } m \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	25, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	21, 29
10	Conditional	value: 11 condition: 12
11	Operation	operator: 26 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 29
14	Literal
15	ExprTuple	17
16	Operation	operator: 18 operands: 19
17	ExprRange	lambda_map: 20 start_index: 24 end_index: 25
18	Literal
19	ExprTuple	21
20	Lambda	parameter: 32 body: 22
21	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
22	Operation	operator: 26 operands: 27
23	Lambda	parameter: 32 body: 28
24	Literal
25	Variable
26	Literal
27	ExprTuple	28, 29
28	IndexedVar	variable: 30 index: 32
29	Variable
30	Variable
31	ExprTuple	32
32	Variable