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Proof step 21 from proof compatarray-mode (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 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))

Rule argument

[crewrite-arg: value-compat , F , [st, ty, val, str] → [st[_mode, val], ty, st[r -- j '], str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- _type ∈ st[_mode, val] ↔ r -- _type ∈ st], [CSIMPSEQ : ⊦ r ≠ jvmref → (st[_mode, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)], [CSIMPSEQ : ⊦ asgcomp(str, val, ty, st) ↔ ¬ is_referencevalue(val) ∨ val .refval = jvmref ∨ is_subtype (str, st[val .refval -- _type] .type, ty)])], [EXTRATERMS : (st[_mode, val], ty, st[r -- j '], str)]]