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Proof step 101 from proof validrefs-subset-equiv (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ validref(str, r, st[r -- _type] .type, st) ↔ ¬ junkref(str, r, st)
Proof step 100:
¬ junkref(str, r, st), st ⊆ st0, validrefs(str, r ' + refs, ty, st0), ∀ 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

[speclemmaarg: ,validref(str, r, st[r -- _type] .type, st) ↔ ¬ junkref(str, r, st) ,[st, r, str] → [st, r, str] ,F ,junkrefs , ,validref-runtimetype ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str)]]