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Proof step 61 from proof sharing-pathex-field-self-01 (previous step)

st[refs0 .last -- _type] .type = mkclasstype(class), st[refs0 .last -- fs '] = refval(r), fs ' ∈ instfields(class), validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ refs0 .last = jvmref, refs0 = [], hasSharing(refs0 .last, st)

User applied rule insert lemma

And obtained the following new goals

Proof step 20:
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 60:
∃ sks. fits((r ' + refs0) .first, sks, st) ∧ 1 + # sks = # (r ' + refs0) ∧ (∀ n. 0 < n ∧ n ≤ # sks → st[(r ' + refs0) .first -- firstn(n, sks)] .refval = (r ' + refs0)[n]), st[refs0 .last -- _type] .type = mkclasstype(class), st[refs0 .last -- fs '] = refval(r), fs ' ∈ instfields(class), validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ refs0 .last = jvmref, refs0 = [], hasSharing(refs0 .last, st)

Rule argument

[x0lemmaarg: spec-name: sharing instance-name: lemma-name: ex-validrefs-fits-stronger antecedent: succedent: substlist: [str, refs, ty, st] → [str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, app-02-ant, ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPNAMEDSEQ : list, references, e, ⊦ r ' ≠ []], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st)]]