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 Conditional, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, FALSE, Forall, InSet, Or, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = Equals(Or(A_1_to_m), FALSE), domain = Set(FALSE)), 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 \left\{\bot\right\}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) = \bot\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: 6
2	Operation	operator: 25 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	24, 7
6	Lambda	parameters: 18 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 34
13	Literal
14	ExprTuple	16
15	Operation	operator: 17 operands: 18
16	ExprRange	lambda_map: 19 start_index: 23 end_index: 24
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 33 body: 21
20	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
21	Operation	operator: 25 operands: 26
22	Lambda	parameter: 33 body: 27
23	Literal
24	Variable
25	Literal
26	ExprTuple	27, 28
27	IndexedVar	variable: 29 index: 33
28	Operation	operator: 31 operand: 34
29	Variable
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	Variable
34	Literal