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Proof step 35 from proof validrefs-junkrefs-append (previous step)

validrefs(str, r ' + refs0, ty, st), junkrefs(str, refs0 .last ' + refs1, st[refs0 .last -- _type] .type, st), ∀ str0, ty0, st0, refs. validrefs(str0, refs0, ty0, st0) ∧ junkrefs(str0, refs0 .last ' + refs, st0[refs0 .last -- _type] .type, st0) → junkrefs(str0, refs0 + refs, ty0, st0) ⊦ refs0 = [], junkrefs(str, (r ' + refs0) + refs1, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st)
Proof step 34:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty)), validrefs(str, r ' + refs0, ty, st), junkrefs(str, refs0 .last ' + refs1, st[refs0 .last -- _type] .type, st), ∀ str0, ty0, st0, refs. validrefs(str0, refs0, ty0, st0) ∧ junkrefs(str0, refs0 .last ' + refs, st0[refs0 .last -- _type] .type, st0) → junkrefs(str0, refs0 + refs, ty0, st0) ⊦ refs0 = [], junkrefs(str, (r ' + refs0) + refs1, ty, st)

Rule argument

[x0lemmaarg: spec-name: junkrefs instance-name: lemma-name: junkrefs-is-junk antecedent: succedent: r ≠ jvmref ∧ ( ¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st) substlist: [st, ty, refs, r, str] → [st, ty, refs0 + refs1, r, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, refs0 + refs1, r, str)]]