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Proof step 70 from proof junkrefs-put-notin-butlast (previous step)

r -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), okval(val, ty0), r ∈ st, ∀ r, fs, st, val, str, ty. r -- fs ' ∈ st ∧ okval(st[r -- fs '], fs .type) ∧ okval(val, fs .type) ∧ r ∈ st → (junkrefs(str, acc + r ', ty, st[r -- fs ', val]) ↔ junkrefs(str, acc + r ', ty, st)) ∨ fs ' = _type ∨ fs ' = _length ∨ r ∈ acc ⊦ mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, junkrefs(str, (r0 ' + acc) + r ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ↔ junkrefs(str, (r0 ' + acc) + r ', ty, st), r = r0, r ∈ acc

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st)
Proof step 66:
¬ (r0 ≠ jvmref ∧ (¬ is_valid_ref(str, r0, st) ∨ ¬ st[r0 -- _type] .type ≤ ty)), r -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), okval(val, ty0), r ∈ st, ∀ r, fs, st, val, str, ty. r -- fs ' ∈ st ∧ okval(st[r -- fs '], fs .type) ∧ okval(val, fs .type) ∧ r ∈ st → (junkrefs(str, acc + r ', ty, st[r -- fs ', val]) ↔ junkrefs(str, acc + r ', ty, st)) ∨ fs ' = _type ∨ fs ' = _length ∨ r ∈ acc ⊦ mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, junkrefs(str, (r0 ' + acc) + r ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ↔ junkrefs(str, (r0 ' + acc) + r ', ty, st), r = r0, r ∈ acc
Proof step 69:
r0 ≠ jvmref ∧ (¬ is_valid_ref(str, r0, st) ∨ ¬ st[r0 -- _type] .type ≤ ty), r -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), okval(val, ty0), r ∈ st, ∀ r, fs, st, val, str, ty. r -- fs ' ∈ st ∧ okval(st[r -- fs '], fs .type) ∧ okval(val, fs .type) ∧ r ∈ st → (junkrefs(str, acc + r ', ty, st[r -- fs ', val]) ↔ junkrefs(str, acc + r ', ty, st)) ∨ fs ' = _type ∨ fs ' = _length ∨ r ∈ acc ⊦ mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, junkrefs(str, (r0 ' + acc) + r ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ↔ true, r = r0, r ∈ acc

Rule argument

[crewrite-arg: junkrefs-is-junk , F , [st, ty, refs, r, str] → [st, ty, acc + r ', r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, acc + r ', r0, str)]]