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Proof step 95 from proof pathex-put-nopathex (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- sk, val]) ⊦ sk = _type, path∃(str, r, r0, st), junkref(str, r, st), path∃(str, r, (r ' + refs0) .last, st)

User applied rule induction

And obtained the following new goals

Proof step 94:
validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- sk, val]), ∀ val, sk, r0, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st[r0 -- sk, val]) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st)) ⊦ sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs0) .last, st)

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, # refs0, [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (# refs0)]]