Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([A_1_to_m], 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(\left(A_{1}, A_{2}, \ldots, A_{m}\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 15 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 33 body: 12
9	ExprRange	lambda_map: 13 start_index: 27 end_index: 28
10	Operation	operator: 14 operands: 15
11	ExprTuple	33
12	Conditional	value: 33 condition: 16
13	Lambda	parameter: 36 body: 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprRange	lambda_map: 23 start_index: 27 end_index: 28
19	Literal
20	ExprTuple	24
21	Literal
22	ExprTuple	32, 25
23	Lambda	parameter: 36 body: 32
24	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
25	Literal
26	Lambda	parameter: 36 body: 29
27	Literal
28	Variable
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	IndexedVar	variable: 34 index: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable