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Proof step 15 from proof ex-validrefs-fits-stronger (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), # sks = # refs1, is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ' + refs1, ty0, st), fits(r0, sks, st), n ≤ 1 + # refs1, ∀ n. n ≠ 0 ∧ ¬ # refs1 < n → st[r0 -- firstn(n, sks)] .refval = (r0 ' + refs1)[n], ∀ st0, ty, r1, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, r1 ' + refs, ty, st0) → (∃ sks. fits(r1, sks, st0) ∧ # sks = # refs ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st0[r1 -- firstn(n, sks)] .refval = (r1 ' + refs)[n]))) ⊦ r = jvmref, st[r -- firstn(n, mkfs(class, ty0, fieldvar) ' ' + sks)] .refval = (r ' + r0 ' + refs1)[n], n = 0, is_arraytype(st[r -- _type] .type), ∃ sks. fits(r, sks, st) ∧ # sks = 1 + # refs1 ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + r0 ' + refs1)[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: n ≠ 0 ,firstn((* n), sk ' + sks) = sk ' + firstn(n -1, sks) ,[sks, sk, n] → [sks, mkfs(class, ty0, fieldvar) ', n] ,F ,list-del ,storekeys ,firstN-num-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks, mkfs(class, ty0, fieldvar) ', n)]]