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Proof step 38 from proof junkrefs-put-badarrayfield (previous step)

is_arraytype(st[r0 -- _type] .type), junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), is_obj(str, r, st) ∨ is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, ty, st, fs, r0, val. ¬ junkrefs(str, acc, ty, st) ∧ fs ' ≠ _type ∧ is_arraytype(st[r0 -- _type] .type) ∧ fs ' ≠ _length → ¬ junkrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + acc, ty, st)

User applied rule case distinction

And obtained the following new goals

Proof step 24:
is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str, ty, st, fs, r0, val. ¬ junkrefs(str, acc, ty, st) ∧ fs ' ≠ _type ∧ is_arraytype(st[r0 -- _type] .type) ∧ fs ' ≠ _length → ¬ junkrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + acc, ty, st)
Proof step 37:
is_array(str, r, st), is_arraytype(st[r0 -- _type] .type), junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str, ty, st, fs, r0, val. ¬ junkrefs(str, acc, ty, st) ∧ fs ' ≠ _type ∧ is_arraytype(st[r0 -- _type] .type) ∧ fs ' ≠ _length → ¬ junkrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + acc, ty, st)

Rule argument

[CASEDARG : pos: left 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]