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Proof step 108 from proof unchanged-junkrefs-level (previous step)

refs0 = r1 + refs, st1[r -- _type] = st[r -- _type], r1 = st[r -- i '] .refval, is_array(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), junkrefs(str, refs0, st[r -- _type] .type .type, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_array(str, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str0, st, st1, str, ty. unchanged(str0, r1, st, st1) ∧ junkrefs(str, refs0, ty, st) ∧ level⊆(str, str0) → junkrefs(str, refs0, ty, st1), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)) ⊦ r = jvmref, refs0 = [], ∃ i. ¬ i < 0 ∧ ¬ st1[r -- _length] .intval ≤ i ∧ is_referencevalue(st1[r -- i ']) ∧ r1 = st1[r -- i '] .refval ∧ junkrefs(str, refs0, st[r -- _type] .type .type, st1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 107:
st1[r -- _type] = st[r -- _type], unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_array(str, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), junkrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ str1, st0, st2, str2, ty0. unchanged(str1, st[r -- i '] .refval, st0, st2) ∧ junkrefs(str2, st[r -- i '] .refval ' + refs, ty0, st0) ∧ level⊆(str2, str1) → junkrefs(str2, st[r -- i '] .refval ' + refs, ty0, st2) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st1[r -- i0 ']) ∧ st[r -- i '] .refval = st1[r -- i0 '] .refval ∧ junkrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, e-01, ⊦ r ' + refs ≠ []], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs])]]