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Proof step 97 from proof validrefs-subset-equiv (previous step)

validrefs(str, r ' + refs, ty, st0), st ⊆ st0, is_valid_ref(str, r, 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)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 96:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st0) ∨ ¬ st0[r -- _type] .type ≤ ty)), validrefs(str, r ' + refs, ty, st0), st ⊆ st0, is_valid_ref(str, r, 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)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, ty, st)

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st0, ty, refs, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, ty, refs, r, str)]]