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Proof step 9 from proof validrefs-applast-array (previous step)

validrefs(str, refs + r ', ty, st) ∧ validrefs(str, r ' + r0 ', st[r -- _type] .type, st) ∧ (refs + r ') .last = (r ' + r0 ') .first ∧ refs + r ' ≠ [] ∧ r ' + r0 ' ≠ [] → validrefs(str, (refs + r ') + (r ' + r0 ') .rest, ty, st), 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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), validrefs(str, r ' + r0 ', st[r -- _type] .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .rest = refs], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + r ') .last = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]