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Proof step 149 from proof compat-addobj (previous step)

st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(i), st[r0 -- j '] = refval(r1), okval(refval(r1), ty0), r0 -- _length ∈ st, is_arrayref(r0, i, st), r0 ∈ st, r0 -- _type ∈ st, compatstatic(str, st), compatmode(str, st), newref(r, st), is_predefined_class(class), 0 ≤ i, j < i, 0 ≤ j, 0 < i, r1 ≠ jvmref → r1 -- _type ∈ st ∧ is_typevalue(st[r1 -- _type]) ∧ is_reftype(st[r1 -- _type] .type) ∧ (has_classtype(st[r1 -- _type] .type) → tdname+∃(str, st[r1 -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[r1 -- _type] .type) → class+∃(str, st[r1 -- _type] .type .class)) ∧ is_subtype(str, st[r1 -- _type] .type, ty0), ¬ has_classtype(ty0) ∨ tdname+∃(str, ty0 .jtelemtype .class), ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → compat(str, st[r0 -- j0 '], ty0, st) ⊦ r0 = jvmref, r = jvmref, compat(str, refval(r1), ty0, st[r -- _type, typeval(mkclasstype(class))])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 144:
⊦ 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 148:
st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(i), st[r0 -- j '] = refval(r1), okval(refval(r1), ty0), r0 -- _length ∈ st, is_arrayref(r0, i, st), r0 ∈ st, r0 -- _type ∈ st, compatstatic(str, st), compatmode(str, st), newref(r, st), is_predefined_class(class), 0 ≤ i, j < i, 0 ≤ j, 0 < i, r1 ≠ jvmref → r1 -- _type ∈ st ∧ is_typevalue(st[r1 -- _type]) ∧ is_reftype(st[r1 -- _type] .type) ∧ (has_classtype(st[r1 -- _type] .type) → tdname+∃(str, st[r1 -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[r1 -- _type] .type) → class+∃(str, st[r1 -- _type] .type .class)) ∧ is_subtype(str, st[r1 -- _type] .type, ty0), ¬ has_classtype(ty0) ∨ tdname+∃(str, ty0 .jtelemtype .class), ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → compat(str, st[r0 -- j0 '], ty0, st) ⊦ r0 = jvmref, r = jvmref, okval(refval(r1), ty0) ∧ ( is_referencevalue(refval(r1)) ∧ refval(r1) .refval ≠ jvmref → refval(r1) .refval -- _type ∈ st[r -- _type, typeval(mkclasstype(class))] ∧ is_typevalue(st[r -- _type, typeval(mkclasstype(class))][refval(r1) .refval -- _type]) ∧ is_reftype((st[r -- _type, typeval(mkclasstype(class))][refval(r1) .refval -- _type]) .type) ∧ ( has_classtype((st[r -- _type, typeval(mkclasstype(class))][refval(r1) .refval -- _type]) .type) → tdname+∃(str, (st[r -- _type, typeval(mkclasstype(class))][refval(r1) .refval -- _type]) .type .jtelemtype .class)) ∧ ( is_classtype((st[r -- _type, typeval(mkclasstype(class))][refval(r1) .refval -- _type]) .type) → class+∃(str, (st[r -- _type, typeval(mkclasstype(class))][refval(r1) .refval -- _type]) .type .class)) ∧ asgcomp(str, refval(r1), ty0, st[r -- _type, typeval(mkclasstype(class))]))

Rule argument

[crewrite-arg: value-compat , F , [st, ty, val, str] → [st[r -- _type, typeval(mkclasstype(class))], ty0, refval(r1), str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- _type, typeval(mkclasstype(class))], ty0, refval(r1), str)]]