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Proof step 26 from proof junkref-subspec-samesubclasses (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs1, ty, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str0, r, st), is_obj(str, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), ∀ str0, str, r1, st0, refs. # refs < # (r0 + refs1) → ( same-subclasses-contains(st0[r1 -- _type] .type .jtelemtype .class, str, str0) ∧ junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → junkref(str0, r1, st0)) ⊦ r = jvmref, junkrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st), junkref(str0, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ¬ junkrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ r ≠ jvmref → (junkrefs(str, r ' + refs, ty, st) ↔ ¬ st[r -- _type] .type ≤ ty)
Proof step 25:
¬ junkrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st) ∧ r0 ≠ jvmref, st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), ¬ st[r0 -- _type] .type ≤ ty, mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str0, r, st), is_obj(str, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), ∀ str0, str, r1, st0, refs. # refs < # (r0 + refs1) → ( same-subclasses-contains(st0[r1 -- _type] .type .jtelemtype .class, str, str0) ∧ junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → junkref(str0, r1, st0)) ⊦ r = jvmref, junkrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st), junkref(str0, r, st)

Rule argument

[speclemmaarg: , ¬ junkrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ r ≠ jvmref → (junkrefs(str, r ' + refs, ty, st) ↔ ¬ st[r -- _type] .type ≤ ty) ,[st, ty, refs, r, str] → [st, ty, refs1, r0, str] ,F ,junkrefs , ,junkrefs-sametype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ junkrefs (str, r ' + refs, st[r -- _type] .type, st) ∧ r ≠ jvmref → ( junkrefs (str, r ' + refs, ty, st) ↔ ¬ st[r -- _type] .type ≤ ty)], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ ¬ junkrefs (str, jvmref ' + refs, ty, st)])], [EXTRATERMS : (st, ty, refs1, r0, str)]]