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, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(m, 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(m \mapsto \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..\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: 38 body: 3
2	ExprTuple	38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 34 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	38, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	31, 18
12	Conditional	value: 13 condition: 14
13	Operation	operator: 26 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18
16	Literal
17	ExprTuple	19, 20, 21, 22
18	ExprRange	lambda_map: 23 start_index: 37 end_index: 38
19	ExprRange	lambda_map: 24 start_index: 37 end_index: 38
20	ExprRange	lambda_map: 25 start_index: 37 end_index: 38
21	Operation	operator: 26 operands: 27
22	ExprRange	lambda_map: 28 start_index: 37 end_index: 38
23	Lambda	parameter: 47 body: 43
24	Lambda	parameter: 47 body: 29
25	Lambda	parameter: 47 body: 30
26	Literal
27	ExprTuple	31
28	Lambda	parameter: 47 body: 32
29	Operation	operator: 34 operands: 33
30	Operation	operator: 34 operands: 35
31	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
32	Operation	operator: 39 operands: 40
33	ExprTuple	42, 41
34	Literal
35	ExprTuple	43, 41
36	Lambda	parameter: 47 body: 42
37	Literal
38	Variable
39	Literal
40	ExprTuple	42, 43
41	Literal
42	IndexedVar	variable: 44 index: 47
43	IndexedVar	variable: 45 index: 47
44	Variable
45	Variable
46	ExprTuple	47
47	Variable