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 And, Boolean, Forall, Implies, InSet, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
expr = Conditional(Forall(instance_param_or_params = [C], instance_expr = C, condition = ExprRange(sub_expr1, Implies(sub_expr2, C), one, m)), And(ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, m), Or(A_1_to_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\{\forall_{C~|~\left(A_{1} \Rightarrow C\right), \left(A_{2} \Rightarrow C\right), \ldots, \left(A_{m} \Rightarrow C\right)}~C \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{m} \in \mathbb{B}\right) ,  A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\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: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 31 body: 10
7	ExprRange	lambda_map: 11 start_index: 25 end_index: 26
8	Operation	operator: 12 operands: 13
9	ExprTuple	31
10	Conditional	value: 31 condition: 14
11	Lambda	parameter: 34 body: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprRange	lambda_map: 21 start_index: 25 end_index: 26
17	Literal
18	ExprTuple	22
19	Literal
20	ExprTuple	30, 23
21	Lambda	parameter: 34 body: 30
22	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
23	Literal
24	Lambda	parameter: 34 body: 27
25	Literal
26	Variable
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	IndexedVar	variable: 32 index: 34
31	Variable
32	Variable
33	ExprTuple	34
34	Variable