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Proof step 18 from proof fits-append (previous step)

∀ r, sks0, st. fits(r, sks1 + sks0, st) ↔ fits(r, sks1, st) ∧ fits(st[r -- sks1] .refval, sks0, st) ⊦ sks1 = [], fits(r, (sk ' + sks1) + sks0, st) ↔ fits(r, sk ' + sks1, st) ∧ fits(st[st[r -- sk] .refval -- sks1] .refval, sks0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 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 17:
∀ r, sks0, st. fits(r, sks1 + sks0, st) ↔ fits(r, sks1, st) ∧ fits(st[r -- sks1] .refval, sks0, st) ⊦ sks1 = [], fits(r, (sk ' + sks1) + sks0, 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, sks1, st) ∧ fits(st[st[r -- sk] .refval -- sks1] .refval, sks0, st)

Rule argument

[crewrite-arg: fits-storekeys-rec , F , [st, sks, sk, r] → [st, sks1, sk, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks1, sk, r)]]