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, B, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m, B_1_to_m
from proveit.logic import Boolean, Forall, Implies, InSet, Not, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(B, sub_expr1)
sub_expr3 = IndexedVar(A, sub_expr1)
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m, B_1_to_m], instance_expr = Or(ExprRange(sub_expr1, Not(sub_expr2), one, m)), domain = Boolean, conditions = [Or(ExprRange(sub_expr1, Not(sub_expr3), one, m)), ExprRange(sub_expr1, Implies(sub_expr3, sub_expr2), 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(m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B_{1}, B_{2}, \ldots, B_{m} \in \mathbb{B}~|~(\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot 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((\lnot B_{1}) \lor  (\lnot B_{2}) \lor  \ldots \lor  (\lnot B_{m})\right) \textrm{ if } m \in \mathbb{N}\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	parameter: 44 body: 3
2	ExprTuple	44
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 40 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	44, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	13, 14
12	Conditional	value: 15 condition: 16
13	ExprRange	lambda_map: 17 start_index: 43 end_index: 44
14	ExprRange	lambda_map: 18 start_index: 43 end_index: 44
15	Operation	operator: 30 operands: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 56 body: 53
18	Lambda	parameter: 56 body: 49
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24, 25, 26
22	ExprRange	lambda_map: 27 start_index: 43 end_index: 44
23	ExprRange	lambda_map: 28 start_index: 43 end_index: 44
24	ExprRange	lambda_map: 29 start_index: 43 end_index: 44
25	Operation	operator: 30 operands: 31
26	ExprRange	lambda_map: 32 start_index: 43 end_index: 44
27	Lambda	parameter: 56 body: 33
28	Lambda	parameter: 56 body: 34
29	Lambda	parameter: 56 body: 35
30	Literal
31	ExprTuple	36
32	Lambda	parameter: 56 body: 37
33	Operation	operator: 50 operand: 49
34	Operation	operator: 40 operands: 39
35	Operation	operator: 40 operands: 41
36	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
37	Operation	operator: 45 operands: 46
38	ExprTuple	49
39	ExprTuple	53, 47
40	Literal
41	ExprTuple	49, 47
42	Lambda	parameter: 56 body: 48
43	Literal
44	Variable
45	Literal
46	ExprTuple	53, 49
47	Literal
48	Operation	operator: 50 operand: 53
49	IndexedVar	variable: 52 index: 56
50	Literal
51	ExprTuple	53
52	Variable
53	IndexedVar	variable: 54 index: 56
54	Variable
55	ExprTuple	56
56	Variable