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Proof step 10 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)

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ validrefs(str, refs, ty, st) ∧ validrefs(str, refs0, ty0, st) ∧ refs .last = refs0 .first ∧ refs ≠ [] ∧ refs0 ≠ [] → validrefs(str, refs + refs0 .rest, ty, st)
Proof step 9:
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)

Rule argument

[LEMMAARG : validrefs-append-01, [str, refs, ty, st, refs0, ty0] → [str, refs + r ', ty, st, r ' + r0 ', st[r -- _type] .type]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, refs + r ', ty, st, r ' + r0 ', st[r -- _type] .type)]]