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Proof step 44 from proof unchNorec-junkrefs (previous step)

¬ (r ≠ jvmref ∧ st[r -- _length] ≠ st0[r -- _length] ∧ is_arraytype(st[r -- _type] .type)), st[r -- _type] = st0[r -- _type], st[r -- i '] = refval(r1), junkrefs(str, r1 ' + refs, st0[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st0), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, unchangedNorec(r, st, st0), st0[r -- _type] .type ≤ ty, ∀ str0, ty0, st1, st2. junkrefs(str0, r1 ' + refs, ty0, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → junkrefs(str0, r1 ' + refs, ty0, st2), ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0) ⊦ r = jvmref, ¬ st0[r -- _length] .intval ≤ i ∧ is_referencevalue(st0[r -- i ']) ∧ r1 = st0[r -- i '] .refval ∧ junkrefs(str, st0[r -- i '] .refval ' + refs, st0[r -- _type] .type .type, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
st[r -- _length] = st0[r -- _length], st[r -- i '] = refval(r1), st[r -- _type] = st0[r -- _type], 0 < st0[r -- _length] .intval, is_arraytype(st0[r -- _type] .type), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), 0 ≤ i, is_array(str, r, st), is_array(str, r, st0), i < st0[r -- _length] .intval, junkrefs(str, r1 ' + refs, st0[r -- _type] .type .type, st), ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0), ∀ str0, ty0, st1, st2. junkrefs(str0, r1 ' + refs, ty0, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → junkrefs(str0, r1 ' + refs, ty0, st2) ⊦ r = jvmref, is_referencevalue(st0[r -- i ']) ∧ r1 = st0[r -- i '] .refval ∧ junkrefs(str, st0[r -- i '] .refval ' + refs, st0[r -- _type] .type .type, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]