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Proof step 55 from proof fits-put-01 (previous step)

r1 ∈ st, is_valid_ref(str, r, st), is_referencevalue(st[r -- (sk ' + sks0)]), okarray(r1, byte_type, st), fits(r, sk ' + sks0, st), ∀ st, r, r1, str, i, by. is_referencevalue(st[r -- sks0]) ∧ okarray(r1, byte_type, st) ∧ fits(r, sks0, st) ∧ r1 ∈ st ∧ is_valid_ref(str, r, st) → r1 = jvmref ∨ r = jvmref ∨ fits(r, sks0, st[r1 -- i ', byteval(by)]) ∨ junkref(str, r, st) ⊦ r1 = jvmref, r = jvmref, junkref(str, r, st), fits(r, sk ' + sks0, st[r1 -- i ', byteval(by)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st)
Proof step 54:
r1 ∈ st, is_valid_ref(str, r, st), is_referencevalue(st[r -- (sk ' + sks0)]), okarray(r1, byte_type, st), r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks0, st), ∀ st, r, r1, str, i, by. is_referencevalue(st[r -- sks0]) ∧ okarray(r1, byte_type, st) ∧ fits(r, sks0, st) ∧ r1 ∈ st ∧ is_valid_ref(str, r, st) → r1 = jvmref ∨ r = jvmref ∨ fits(r, sks0, st[r1 -- i ', byteval(by)]) ∨ junkref(str, r, st) ⊦ r1 = jvmref, r = jvmref, junkref(str, r, st), fits(r, sk ' + sks0, st[r1 -- i ', byteval(by)])

Rule argument

[crewrite-arg: fits-storekeys-rec , F , [st, sks, sk, r] → [st, sks0, sk, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks0, sk, r)]]