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Proof step 56 from proof unchanged-junkrefs-level (previous step)

st1[r -- _type] = st[r -- _type], refs0 .first = st[r -- fs '] .refval, is_obj(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs ']), junkrefs(str, refs0, fs .type, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_obj(str, r, st), ∀ str0, st, st1, str, ty. unchanged(str0, refs0 .first, st, st1) ∧ junkrefs(str, refs0, ty, st) ∧ level⊆(str, str0) → junkrefs(str, refs0, ty, st1), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)) ⊦ r = jvmref, refs0 = [], ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs ']) ∧ refs0 .first = st1[r -- fs '] .refval ∧ junkrefs(str, refs0, fs .type, st1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
refs0 = r1 + refs, st1[r -- _type] = st[r -- _type], r1 = st[r -- fs '] .refval, is_obj(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs ']), junkrefs(str, refs0, fs .type, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_obj(str, r, st), ∀ str0, st, st1, str, ty. unchanged(str0, r1, st, st1) ∧ junkrefs(str, refs0, ty, st) ∧ level⊆(str, str0) → junkrefs(str, refs0, ty, st1), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)) ⊦ r = jvmref, refs0 = [], ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs ']) ∧ r1 = st1[r -- fs '] .refval ∧ junkrefs(str, refs0, fs .type, st1)

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: references lemma-name: elim-list-c antecedent: refs ≠ [] succedent: r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 substlist: [refs, r, refs0] → [refs0, r1, refs] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs0, r1, refs)]]