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Proof step 113 from proof unchanged-junkrefs-level (previous step)

st1[r -- _type] = st[r -- _type], is_array(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, junkrefs(str, r ' + refs0, ty, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_array(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, junkrefs(str, r ' + refs0, ty, st1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ junkrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 64:
⊦ unchangedNorec(r, st, st0) ∧ is_array(str, r, st) → (¬ is_array(str, r, st0) ↔ false)
Proof step 112:
is_array(str, r, st1) ∧ st1[r -- _type] .type ≤ ty, st1[r -- _type] = st[r -- _type], is_array(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, junkrefs(str, r ' + refs0, ty, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_array(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 ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st1[r -- _length] .intval ∧ is_referencevalue(st1[r -- i ']) ∧ refs0 .first = st1[r -- i '] .refval ∧ junkrefs(str, refs0, st1[r -- _type] .type .type, st1))

Rule argument

[x0lemmaarg: spec-name: junkrefs instance-name: lemma-name: junkrefs-array antecedent: succedent: is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ junkrefs (str, refs, st[r -- _type] .type .type, st))) substlist: [st, ty, refs, r, str] → [st1, ty, refs0, 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 : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st1, ty, refs0, r, str)]]