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Proof step 22 from proof validrefs-trans-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ', st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, r0 ' + refs1, ty0, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ', ty1, st0) ∧ validrefs(str0, r0 ' + refs, ty2, st0) → validrefs(str0, r0 ' + refs, ty1, st0) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs1, ty, st)

Rule argument

[emptyarg]

Additional information

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