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Proof step 52 from proof unchNorec-junkrefs (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- _type] = st0[r -- _type], is_array(str, r, st0), refs0 ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ junkrefs(str, refs0, st[r -- _type] .type .type, st)), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0), ∀ str, ty, st, st0. junkrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → junkrefs(str, refs0, ty, st0) ⊦ r = jvmref, refs0 ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i ∧ is_referencevalue(st0[r -- i ']) ∧ refs0 .first = st0[r -- i '] .refval ∧ junkrefs(str, refs0, st0[r -- _type] .type .type, st0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
st[r -- _type] = st0[r -- _type], refs0 .first = st[r -- i '] .refval, is_array(str, r, st), is_array(str, r, st0), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), junkrefs(str, refs0, st0[r -- _type] .type .type, st), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0), ∀ str, ty, st, st0. junkrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → junkrefs(str, refs0, ty, st0) ⊦ r = jvmref, refs0 = [], ∃ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i ∧ is_referencevalue(st0[r -- i ']) ∧ refs0 .first = st0[r -- i '] .refval ∧ junkrefs(str, refs0, st0[r -- _type] .type .type, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j])]]