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 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], instance_expr = Forall(instance_param_or_params = [C], instance_expr = C, condition = ExprRange(sub_expr1, Implies(IndexedVar(A, sub_expr1), C), one, m)), domain = Boolean, condition = Or(A_1_to_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} \in \mathbb{B}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}}~\left[\forall_{C~|~\left(A_{1} \Rightarrow C\right), \left(A_{2} \Rightarrow C\right), \ldots, \left(A_{m} \Rightarrow C\right)}~C\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: 36 body: 3
2	ExprTuple	36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 13 operand: 8
5	Operation	operator: 29 operands: 7
6	ExprTuple	8
7	ExprTuple	36, 9
8	Lambda	parameters: 23 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 16
12	Operation	operator: 27 operands: 15
13	Literal
14	ExprTuple	16
15	ExprTuple	17, 18
16	Lambda	parameter: 41 body: 20
17	ExprRange	lambda_map: 21 start_index: 35 end_index: 36
18	Operation	operator: 22 operands: 23
19	ExprTuple	41
20	Conditional	value: 41 condition: 24
21	Lambda	parameter: 44 body: 25
22	Literal
23	ExprTuple	26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprRange	lambda_map: 31 start_index: 35 end_index: 36
27	Literal
28	ExprTuple	32
29	Literal
30	ExprTuple	40, 33
31	Lambda	parameter: 44 body: 40
32	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
33	Literal
34	Lambda	parameter: 44 body: 37
35	Literal
36	Variable
37	Operation	operator: 38 operands: 39
38	Literal
39	ExprTuple	40, 41
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable