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Proof step 81 from proof ex-fits-validrefs-stronger (previous step)

# refs = # sks0, st[r -- sk] = refval(r0), validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), fits(r0, sks0, st), sks ⊑ sk ' + sks0, ∀ sks1. sks1 ⊑ sks0 ∧ sks1 ≠ [] → st[r0 -- sks1] .refval = (r0 ' + refs)[# sks1], is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st) ∨ is_array(str, r, st) ⊦ r = jvmref, sks = [], st[r -- sks] .refval = (r ' + r0 ' + refs)[# sks], junkref(str, r, st), junkref(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
⊦ sks ≠ [] → (sks ⊑ sk ' + sks0 ↔ sks .first = sk ∧ sks .rest ⊑ sks0)
Proof step 80:
sks ≠ [], # refs = # sks0, st[r -- sk] = refval(r0), validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), fits(r0, sks0, st), sks .first = sk ∧ sks .rest ⊑ sks0, ∀ sks1. sks1 ⊑ sks0 ∧ sks1 ≠ [] → st[r0 -- sks1] .refval = (r0 ' + refs)[# sks1], is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st) ∨ is_array(str, r, st) ⊦ r = jvmref, sks = [], st[r -- sks] .refval = (r ' + r0 ' + refs)[# sks], junkref(str, r, st), junkref(str, r0, st)

Rule argument

[speclemmaarg: ,sks ≠ [] → (sks ⊑ sk ' + sks0 ↔ sks .first = sk ∧ sks .rest ⊑ sks0) ,[sks0, sk, sks] → [sks0, sk, sks] ,F ,list-last ,storekeys ,prefix-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks0, sk, sks)]]