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Proof step 5 from proof validrefs-applast-array (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
st[r -- i '] = refval(r0), validrefs(str, refs + r ', ty, st), is_array(str, r, st), i < st[r -- _length] .intval, st[r0 -- _type] .type ≤ st[r -- _type] .type .type, is_valid_ref(str, r0, st), type∃(str, st[r0 -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ validrefs(str, refs + r ' + r0 ', ty, st), validrefs(str, r0 ', st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]