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Proof step 8 from proof compatarray-mode (previous step)

st[r -- _type] .type = mkarraytype(ty), st[r -- _length] = intval(i), st[r -- j '] = refval(r0), j < i, 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r ∈ st, 0 ≤ j, 0 < i, okval(refval(r0), ty), r0 ≠ jvmref → r0 -- _type ∈ st ∧ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ∧ (has_classtype(st[r0 -- _type] .type) → tdname+∃(str, st[r0 -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[r0 -- _type] .type) → class+∃(str, st[r0 -- _type] .type .class)) ∧ is_subtype(str, st[r0 -- _type] .type, ty) ⊦ r = jvmref, compat(str, refval(r0), ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ compat(str, val, ty, st) ↔ okval(val, ty) ∧ ( is_referencevalue(val) ∧ val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ is_reftype(st[val .refval -- _type] .type) ∧ (has_classtype(st[val .refval -- _type] .type) → tdname+∃(str, st[val .refval -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[val .refval -- _type] .type) → class+∃(str, st[val .refval -- _type] .type .class)) ∧ asgcomp(str, val, ty, st))
Proof step 7:
st[r -- _type] .type = mkarraytype(ty), st[r -- _length] = intval(i), st[r -- j '] = refval(r0), j < i, 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r ∈ st, 0 ≤ j, 0 < i, okval(refval(r0), ty), r0 ≠ jvmref → r0 -- _type ∈ st ∧ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ∧ (has_classtype(st[r0 -- _type] .type) → tdname+∃(str, st[r0 -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[r0 -- _type] .type) → class+∃(str, st[r0 -- _type] .type .class)) ∧ is_subtype(str, st[r0 -- _type] .type, ty) ⊦ r = jvmref, okval(refval(r0), ty) ∧ ( is_referencevalue(refval(r0)) ∧ refval(r0) .refval ≠ jvmref → refval(r0) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r0) .refval -- _type]) ∧ is_reftype(st[refval(r0) .refval -- _type] .type) ∧ (has_classtype(st[refval(r0) .refval -- _type] .type) → tdname+∃(str, st[refval(r0) .refval -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[refval(r0) .refval -- _type] .type) → class+∃(str, st[refval(r0) .refval -- _type] .type .class)) ∧ asgcomp(str, refval(r0), ty, st))

Rule argument

[crewrite-arg: value-compat , F , [st, ty, val, str] → [st, ty, refval(r0), str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, refval(r0), str)]]