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Proof step 79 from proof ex-fits-validrefs-stronger (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 78:
sks = sk + sks2, # refs = # sks0, st[r -- sk] = refval(r0), validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), fits(r0, sks0, st), sks2 ⊑ 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, st[r -- sks] .refval = (r ' + r0 ' + refs)[# sks], sks = [], junkref(str, r, st), junkref(str, r0, st)

Rule argument

[speclemmaarg: sks ≠ [] ,sk = sks .first ∧ sks0 = sks .rest ↔ sks = sk + sks0 ,[sks, sk, sks0] → [sks, sk, sks2] ,T ,list-data ,storekeys ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : sks ≠ [] ⊦ sk = sks .first ∧ sks0 = sks .rest ↔ sks = sk + sks0])], [EXTRATERMS : (sks, sk, sks2)]]