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Proof step 20 from proof disjoint-nojunk-newref-subset-01 (previous step)

(r1 ' + refs1) .last = (r ' + refs0) .last, validrefs(str, r ' + refs0, st1[r -- _type] .type, st1), validrefs(str, r1 ' + refs1, st1[r1 -- _type] .type, st), newref(r, st), st ⊆ st1 ⊦ (r ' + refs0) .last = jvmref, r = jvmref, r1 = r, path∃(str, r, (r ' + refs0) .last, st1), junkref(str, r1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk]
Proof step 19:
r1 -- _type ∈ st ∧ st ⊆ st1, (r1 ' + refs1) .last = (r ' + refs0) .last, validrefs(str, r ' + refs0, st1[r -- _type] .type, st1), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st), newref(r, st), st ⊆ st1 ⊦ (r ' + refs0) .last = jvmref, r = jvmref, r1 = r, path∃(str, r, (r ' + refs0) .last, st1), junkref(str, r1, st)

Rule argument

[x0lemmaarg: spec-name: store instance-name: javastore lemma-name: superset-elem-eq antecedent: succedent: rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk] substlist: [rk, st, st1] → [r1 -- _type, st, st1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2, 1, 2, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r -- _type ∈ st → ( junkref(str, r, st) ↔ r ≠ jvmref)], [CSIMPSEQ : ⊦ validrefs (str, jvmref ' + refs, ty, st) ↔ refs = []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ r ' .last = r])], [EXTRATERMS : (r1 -- _type, st, st1)]]