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Proof step 75 from proof junkrefs-put-nopathexplus-equiv (previous step)

st[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ val, sk, r, st0, ty, r2, str, refs. # refs < # (r0 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r, st0)) ⊦ r = r0, sk = _type, r = jvmref, junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), r ≠ jvmref ∧ is_classtype(st[r -- _type] .type) ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval = r0) ∨ is_arraytype(st[r -- _type] .type) ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval = r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 74:
st[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), st[r -- _type] .type ≤ ty, is_arraytype(st[r -- _type] .type), ∀ val, sk, r, st0, ty, r2, str, refs. # refs < # (r0 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r, st0)) ⊦ r = r0, sk = _type, r = jvmref, junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i0 '] .refval = r0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ ¬ is_classtype(ty) ∧ ¬ is_arraytype(ty) → (ty ≤ ty0 ↔ ty = ty0)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_classtype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]