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, B, Conditional, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m, B_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, B_1_to_m], instance_expr = Or(B_1_to_m), domain = Boolean, conditions = [Or(A_1_to_m), ExprRange(sub_expr1, Implies(IndexedVar(A, sub_expr1), IndexedVar(B, sub_expr1)), one, 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}, B_{1}, B_{2}, \ldots, B_{m} \in \mathbb{B}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m},\left(A_{1} \Rightarrow B_{1}\right), \left(A_{2} \Rightarrow B_{2}\right), \ldots, \left(A_{m} \Rightarrow B_{m}\right)}~\left(B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\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: 31 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	35, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	28, 15
9	Conditional	value: 10 condition: 11
10	Operation	operator: 23 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15
13	Literal
14	ExprTuple	16, 17, 18, 19
15	ExprRange	lambda_map: 20 start_index: 34 end_index: 35
16	ExprRange	lambda_map: 21 start_index: 34 end_index: 35
17	ExprRange	lambda_map: 22 start_index: 34 end_index: 35
18	Operation	operator: 23 operands: 24
19	ExprRange	lambda_map: 25 start_index: 34 end_index: 35
20	Lambda	parameter: 44 body: 40
21	Lambda	parameter: 44 body: 26
22	Lambda	parameter: 44 body: 27
23	Literal
24	ExprTuple	28
25	Lambda	parameter: 44 body: 29
26	Operation	operator: 31 operands: 30
27	Operation	operator: 31 operands: 32
28	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
29	Operation	operator: 36 operands: 37
30	ExprTuple	39, 38
31	Literal
32	ExprTuple	40, 38
33	Lambda	parameter: 44 body: 39
34	Literal
35	Variable
36	Literal
37	ExprTuple	39, 40
38	Literal
39	IndexedVar	variable: 41 index: 44
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable