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Proof step 120 from proof compat-put (previous step)

st[r0 -- _type] = typeval(mkarraytype(ty1)), compat(str, val, ty, st), compatstatic(str, st), compatmode(str, st), r0 -- _type ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 -- _type ∈ st, r0 ∈ st, ¬ has_classtype(ty1) ∨ tdname+∃(str, ty1 .jtelemtype .class), ¬ has_classtype(ty1) ∨ class∃(str, ty1 .jtelemtype .class) ∨ interface∃(str, ty1 .jtelemtype .class) ∨ is_predefined_class(ty1 .jtelemtype .class) → compatarray(str, r0, st) ⊦ r0 = jvmref, ty = void_type, mkfs(class, ty, fieldvar) ' = _length, compatarray(str, r0, st[r -- mkfs(class, ty, fieldvar) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 108:
⊦ compatarray(str, r, st) ↔ is_arraytype(st[r -- _type] .type) ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → compat(str, st[r -- j '], st[r -- _type] .type .type, st))
Proof step 119:
st[r0 -- _type] = typeval(mkarraytype(ty1)), compat(str, val, ty, st), compatstatic(str, st), compatmode(str, st), r0 -- _type ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 -- _type ∈ st, r0 ∈ st, ¬ has_classtype(ty1) ∨ tdname+∃(str, ty1 .jtelemtype .class), ¬ has_classtype(ty1) ∨ class∃(str, ty1 .jtelemtype .class) ∨ interface∃(str, ty1 .jtelemtype .class) ∨ is_predefined_class(ty1 .jtelemtype .class) → compatarray(str, r0, st) ⊦ r0 = jvmref, ty = void_type, mkfs(class, ty, fieldvar) ' = _length, is_arraytype((st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- _type]) .type) ∧ r0 -- _length ∈ st[r -- mkfs(class, ty, fieldvar) ', val] ∧ is_integervalue(st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- _length]) ∧ 0 ≤ (st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- _length]) .intval ∧ is_arrayref(r0, (st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- _length]) .intval, st[r -- mkfs(class, ty, fieldvar) ', val]) ∧ (∀ j. 0 ≤ j ∧ j < (st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- _length]) .intval → compat (str, st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- j '], (st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- _type]) .type .type, st[r -- mkfs(class, ty, fieldvar) ', val]))

Rule argument

[crewrite-arg: array-compat , F , [st, r, str] → [st[r -- mkfs(class, ty, fieldvar) ', val], r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- mkfs(class, ty, fieldvar) ', val], r0, str)]]