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Proof step 103 from proof validrefs-subset-equiv (previous step)

validrefs(str, r ' + refs, ty, st0), st ⊆ st0, validref(str, r, st[r -- _type] .type, st) ⊦ validrefs(str, r ' + refs, ty, st)

User applied rule induction

And obtained the following new goals

Proof step 102:
validrefs(str, r ' + refs, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st), ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ validrefs(str, r ' + refs, ty, st)

Rule argument

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

Additional information

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