**Description: **(*Note*: This
inference rule and the previous one, idi 1, will
normally never appear in a completed proof.)
This is a technical inference to assist proof development. It provides
a temporary way to add an independent subproof to a proof under
development, for later assignment to a normal proof step.
The Metamath (Metamath-exe) program Proof Assistant requires proofs to
be developed backwards from the conclusion with no gaps, and it has no
mechanism that lets the user work on isolated subproofs. This inference
provides a workaround for this limitation. It can be inserted at any
point in a proof to allow an independent subproof to be developed on the
side, for later use as part of the final proof.
*Instructions*: (1) Assign this inference to any unknown step in
the
proof. Typically, the last unknown step is the most convenient, since
"MM-PA> ASSIGN LAST" can be used. This step will be
replicated in
hypothesis a1ii.1, from where the development of the main proof can
continue. (2) Develop the independent subproof backwards from
hypothesis a1ii.2. If desired, use a "MM-PA> LET STEP"
command to
pre-assign the conclusion of the independent subproof to a1ii.2. (3)
After the independent subproof is complete, use "MM-PA> IMPROVE
ALL" to
assign it automatically to an unknown step in the main proof that
matches it. (4) After the entire proof is complete, use "MM-PA>
MINIMIZE_WITH *" to clean up (discard) all a1ii 2
references
automatically.
This inference was originally designed to assist importing partially
completed Proof Worksheets from the mmj2 Proof Assistant GUI, but it can
also be useful on its own. Interestingly, no axioms are required for
its proof. It is the inference associated with a1i 9.
(Contributed by
NM, 7-Feb-2006.) (Proof modification is discouraged.)
(New usage is discouraged.) |