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Proof step 28 from proof sharing-twopaths (previous step)

st[r -- sks0] = refval(refs0 .last), st[r -- sks] = refval(r0), fits(r, sks0, st), fits(r, sks, st), validrefs(str, r0 ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ refs0 = [], r = jvmref, sks = sks0, sks = [], sks0 = [], r0 = jvmref, refs0 .last = jvmref, sks ⊑ sks0, hasSharing(r, st)

User applied rule insert lemma

And obtained the following new goals

Proof step 10:
validrefs(str, refs, ty, st), refs ≠ [] ⊦ ∃ sks. fits(refs .first, sks, st) ∧ 1 + # sks = # refs ∧ (∀ n. 0 < n ∧ n ≤ # sks → st[refs .first -- firstn(n, sks)] .refval = refs[n])
Proof step 27:
∃ sks. fits((r0 ' + refs0) .first, sks, st) ∧ 1 + # sks = # (r0 ' + refs0) ∧ (∀ n. 0 < n ∧ n ≤ # sks → st[(r0 ' + refs0) .first -- firstn(n, sks)] .refval = (r0 ' + refs0)[n]), st[r -- sks0] = refval(refs0 .last), st[r -- sks] = refval(r0), fits(r, sks0, st), fits(r, sks, st), validrefs(str, r0 ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ refs0 = [], r = jvmref, sks = sks0, sks = [], sks0 = [], r0 = jvmref, refs0 .last = jvmref, sks ⊑ sks0, hasSharing(r, st)

Rule argument

[LEMMAARG : ex-validrefs-fits-stronger, [str, refs, ty, st] → [str, r0 ' + refs0, mkclasstype(`java.lang.Object' .class), st]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, r0 ' + refs0, mkclasstype(`java.lang.Object' .class), st)]]