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Proof step 75 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), 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), sks2 ≠ [] → st[r0 -- sks2] .refval = (r0 ' + refs)[# sks2] ⊦ r = jvmref, st[r -- (sk ' + sks2)] .refval = (r0 ' + refs)[# sks2], junkref(str, r, st), junkref(str, r0, st)

User applied rule cut formula

And obtained the following new goals

Proof step 74:
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), sks2 ≠ [] → st[r0 -- sks2] .refval = (r0 ' + refs)[# sks2] ⊦ r = jvmref, st[r -- (sk ' + sks2)] .refval = (r0 ' + refs)[# sks2], junkref(str, r, st), junkref(str, r0, st)

Rule argument

[fma-arg: sks2 ≠ []]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sks + [] = sks], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ st[r -- sk '] = st[r -- sk]], [CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ (r ' + refs)[0] = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ [] ⊑ sks], [CSIMPSEQ : ⊦ refval(r) .refval = r])], [EXTRAFMAS : (sks2 ≠ [])]]