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binghe committed Oct 1, 2024
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10 changes: 5 additions & 5 deletions examples/lambda/barendregt/boehmScript.sml
Original file line number Diff line number Diff line change
Expand Up @@ -3266,7 +3266,7 @@ Proof
>> qexistsl_tac [‘X’, ‘M0’, ‘r’, ‘d’] >> rw []
QED

Theorem subterm_width_recursion :
Theorem subterm_width_induction_lemma :
!X M h p r M0 n m vs M1 Ms d.
FINITE X /\ FV M SUBSET X UNION RANK r /\
h::p IN ltree_paths (BT' X M r) /\
Expand Down Expand Up @@ -3598,10 +3598,10 @@ Proof
Q.PAT_X_ASSUM ‘args' = Ms’ (fs o wrap o SYM) \\
Q.PAT_X_ASSUM ‘m' = m’ (fs o wrap o SYM) \\
fs [Abbr ‘m'’] >> T_TAC \\
(* applying subterm_width_recursion *)
(* applying subterm_width_induction_lemma *)
Know ‘subterm_width ([P/v] M) (h::q) <= d <=>
m <= d /\ subterm_width (EL h args') q <= d’
>- (MATCH_MP_TAC subterm_width_recursion \\
>- (MATCH_MP_TAC subterm_width_induction_lemma \\
qexistsl_tac [‘X’, ‘r’, ‘M0'’, ‘n’, ‘vs’, ‘VAR y @* args'’] \\
simp [principle_hnf_beta_reduce] \\
CONJ_TAC
Expand Down Expand Up @@ -3763,10 +3763,10 @@ Proof
>> ‘M1' = VAR z' @* (args' ++ ls)’ by METIS_TAC [principle_hnf_thm]
>> Q.PAT_X_ASSUM ‘M0' @* MAP VAR vs @* MAP VAR ys -h->* _’ K_TAC
>> qabbrev_tac ‘P = permutator d’
(* applying subterm_width_recursion again *)
(* applying subterm_width_induction_lemma again *)
>> Know ‘subterm_width ([P/y] M) (h::q) <= d <=>
m' <= d /\ subterm_width (EL h Ms) q <= d’
>- (MATCH_MP_TAC subterm_width_recursion \\
>- (MATCH_MP_TAC subterm_width_induction_lemma \\
qexistsl_tac [‘X’, ‘r’, ‘M0'’, ‘n'’, ‘vs'’, ‘M1'’] \\
simp [appstar_APPEND] \\
CONJ_TAC
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