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Proof step 22 from proof disjoint-def-fits (previous step)

st[r0 -- sks0] = refval(r1), st[r -- sks] = refval(r1), validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st), fits(r, sks, st), fits(r0, sks0, st), r ∈ refs, r0 ∈ refs, ∀ refs0, refs1. refs0 = [] ∨ refs1 = [] ∨ ¬ refs0 .first ∈ refs ∨ ¬ refs1 .first ∈ refs ∨ refs0 .first = refs1 .first ∨ refs0 .last ≠ refs1 .last ∨ refs0 .last = jvmref ∨ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∨ ¬ validrefs(str, refs1, st[refs1 .first -- _type] .type, st) ⊦ r1 = jvmref, r0 = r

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
¬ junkref(str, r, st), fits(r, sks, st) ⊦ ∃ refs. validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ st[r -- sks] .refval = (r ' + refs) .last
Proof step 9:
st[r0 -- sks0] = refval(r1), st[r -- sks] = refval(r1), validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st), fits(r, sks, st), fits(r0, sks0, st), r ∈ refs, r0 ∈ refs, ∀ refs0, refs1. refs0 = [] ∨ refs1 = [] ∨ ¬ refs0 .first ∈ refs ∨ ¬ refs1 .first ∈ refs ∨ refs0 .first = refs1 .first ∨ refs0 .last ≠ refs1 .last ∨ refs0 .last = jvmref ∨ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∨ ¬ validrefs(str, refs1, st[refs1 .first -- _type] .type, st) ⊦ ¬ junkref(str, r0, st), r1 = jvmref, r0 = r
Proof step 21:
∃ refs. validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) ∧ st[r0 -- sks0] .refval = (r0 ' + refs) .last, st[r0 -- sks0] = refval(r1), st[r -- sks] = refval(r1), validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st), fits(r, sks, st), fits(r0, sks0, st), r ∈ refs, r0 ∈ refs, ∀ refs0, refs1. refs0 = [] ∨ refs1 = [] ∨ ¬ refs0 .first ∈ refs ∨ ¬ refs1 .first ∈ refs ∨ refs0 .first = refs1 .first ∨ refs0 .last ≠ refs1 .last ∨ refs0 .last = jvmref ∨ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∨ ¬ validrefs(str, refs1, st[refs1 .first -- _type] .type, st) ⊦ r1 = jvmref, r0 = r

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: ex-fits-validrefs antecedent: ¬ junkref(str, r, st), fits(r, sks, st) succedent: ∃ refs. validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ st[r -- sks] .refval = (r ' + refs) .last substlist: [str, r, st, sks] → [str, r0, st, sks0] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r0, st, sks0)]]