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Proof step 27 from proof validrefs-trans-01 (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, refs0 .last ' + refs1, ty0, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ' + refs0, ty1, st0) ∧ validrefs(str0, refs0 .last ' + refs, ty2, st0) → validrefs(str0, (r0 ' + refs0) + refs, ty1, st0) ⊦ refs0 = [], r = jvmref, (r0 ' + refs0) + refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ ((r0 ' + refs0) + refs1) .first = st[r -- i '] .refval ∧ validrefs(str, (r0 ' + refs0) + refs1, st[r -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, refs0 .last ' + refs1, ty0, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ' + refs0, ty1, st0) ∧ validrefs(str0, refs0 .last ' + refs, ty2, st0) → validrefs(str0, (r0 ' + refs0) + refs, ty1, st0) ⊦ refs0 = [], r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval ∧ validrefs(str, (st[r -- i0 '] .refval ' + refs0) + refs1, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []])]]