Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 37 body: 2
1	ExprTuple	37
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 33 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	37, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	30, 17
11	Conditional	value: 12 condition: 13
12	Operation	operator: 25 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17
15	Literal
16	ExprTuple	18, 19, 20, 21
17	ExprRange	lambda_map: 22 start_index: 36 end_index: 37
18	ExprRange	lambda_map: 23 start_index: 36 end_index: 37
19	ExprRange	lambda_map: 24 start_index: 36 end_index: 37
20	Operation	operator: 25 operands: 26
21	ExprRange	lambda_map: 27 start_index: 36 end_index: 37
22	Lambda	parameter: 46 body: 42
23	Lambda	parameter: 46 body: 28
24	Lambda	parameter: 46 body: 29
25	Literal
26	ExprTuple	30
27	Lambda	parameter: 46 body: 31
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
31	Operation	operator: 38 operands: 39
32	ExprTuple	41, 40
33	Literal
34	ExprTuple	42, 40
35	Lambda	parameter: 46 body: 41
36	Literal
37	Variable
38	Literal
39	ExprTuple	41, 42
40	Literal
41	IndexedVar	variable: 43 index: 46
42	IndexedVar	variable: 44 index: 46
43	Variable
44	Variable
45	ExprTuple	46
46	Variable