Expression of type Conditional

from the theory of proveit.logic.booleans.disjunction

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 A, C, Conditional, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Boolean, Forall, Implies, InSet, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = Forall(instance_param_or_params = [C], instance_expr = C, condition = ExprRange(sub_expr1, Implies(IndexedVar(A, sub_expr1), C), one, m)), domain = Boolean, condition = Or(A_1_to_m)), InSet(m, Natural))

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} \in \mathbb{B}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}}~\left[\forall_{C~|~\left(A_{1} \Rightarrow C\right), \left(A_{2} \Rightarrow C\right), \ldots, \left(A_{m} \Rightarrow C\right)}~C\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: 10 operand: 5
2	Operation	operator: 26 operands: 4
3	ExprTuple	5
4	ExprTuple	33, 6
5	Lambda	parameters: 20 body: 7
6	Literal
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 24 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	14, 15
13	Lambda	parameter: 38 body: 17
14	ExprRange	lambda_map: 18 start_index: 32 end_index: 33
15	Operation	operator: 19 operands: 20
16	ExprTuple	38
17	Conditional	value: 38 condition: 21
18	Lambda	parameter: 41 body: 22
19	Literal
20	ExprTuple	23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprRange	lambda_map: 28 start_index: 32 end_index: 33
24	Literal
25	ExprTuple	29
26	Literal
27	ExprTuple	37, 30
28	Lambda	parameter: 41 body: 37
29	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
30	Literal
31	Lambda	parameter: 41 body: 34
32	Literal
33	Variable
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37, 38
37	IndexedVar	variable: 39 index: 41
38	Variable
39	Variable
40	ExprTuple	41
41	Variable