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Proof step 23 from proof validrefs-superclass (previous step)

acc = r0 + refs, r0 = st[r -- i '] .refval, is_array(str, r, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, acc, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ ty, ty0, str, st. ty ≤ ty0 ∧ validrefs(str, acc, ty, st) → validrefs(str, acc, ty0, st) ⊦ r = jvmref, acc = [], ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st), ∀ ty1, ty2, str0, st0. ty1 ≤ ty2 ∧ validrefs(str0, st[r -- i '] .refval ' + refs, ty1, st0) → validrefs(str0, st[r -- i '] .refval ' + refs, ty2, st0) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i '] .refval = st[r -- i0 '] .refval

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]