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, Conditional, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Equals, FALSE, InSet, Or, Set
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Or(A_1_to_m), FALSE), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Set(FALSE)), one, m)))

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\{\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) = \bot \textrm{ if } \left(A_{1} \in \left\{\bot\right\}\right) \land  \left(A_{2} \in \left\{\bot\right\}\right) \land  \ldots \land  \left(A_{m} \in \left\{\bot\right\}\right)\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 26
5	Literal
6	ExprTuple	8
7	Operation	operator: 9 operands: 10
8	ExprRange	lambda_map: 11 start_index: 15 end_index: 16
9	Literal
10	ExprTuple	12
11	Lambda	parameter: 25 body: 13
12	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
13	Operation	operator: 17 operands: 18
14	Lambda	parameter: 25 body: 19
15	Literal
16	Variable
17	Literal
18	ExprTuple	19, 20
19	IndexedVar	variable: 21 index: 25
20	Operation	operator: 23 operand: 26
21	Variable
22	ExprTuple	25
23	Literal
24	ExprTuple	26
25	Variable
26	Literal