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Proof step 57 from proof junkrefs-put-notin-butlast (previous step)

acc + r ' = r1 ' + refs, is_array(str, r0, st), r -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), okval(val, ty0), r ∈ st, st[r0 -- _type] .type ≤ ty, ∀ 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 ⊦ r = r0, r0 = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st)), r ∈ acc, ¬ r1 ∈ acc ∧ r1 ≠ r, r ≠ r1 ∧ ¬ r ∈ refs

User applied rule case distinction

And obtained the following new goals

Proof step 49:
∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val]), acc + r ' = r1 ' + refs, is_array(str, r0, st), r -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), okval(val, ty0), r ∈ st, st[r0 -- _type] .type ≤ ty, ∀ 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 ⊦ ∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st), r = r0, r0 = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, ¬ r1 ∈ acc ∧ r1 ≠ r, r ≠ r1 ∧ ¬ r ∈ refs
Proof step 56:
∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st), acc + r ' = r1 ' + refs, is_array(str, r0, st), r -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), okval(val, ty0), r ∈ st, st[r0 -- _type] .type ≤ ty, ∀ 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 ⊦ ∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val]), r = r0, r0 = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, ¬ r1 ∈ acc ∧ r1 ≠ r, r ≠ r1 ∧ ¬ r ∈ refs

Rule argument

[CASEDARG : pos: right 5, ()]

Additional information

[[CONCRETESIMPRULES : ()]]