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Proof step 32 from proof disjoint-def-fits (previous step)

(r1 ' + refs2) .last = (r2 ' + refs1) .last, st[r2 -- sks] = refval((r2 ' + refs1) .last), fits(r2, sks, st), validrefs(str, r2 ' + refs1, st[r2 -- _type] .type, st), validrefs(str, r1 ' + refs2, st[r1 -- _type] .type, st), r2 ∈ refs, r1 ∈ refs, validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st), ∀ r, sks, r0, sks0. ¬ r ∈ refs ∨ ¬ r0 ∈ refs ∨ r = r0 ∨ ¬ fits(r, sks, st) ∨ ¬ fits(r0, sks0, st) ∨ st[r -- sks] ≠ st[r0 -- sks0] ∨ st[r -- sks] .refval = jvmref ⊦ (r2 ' + refs1) .last = jvmref, r1 = r2

User applied rule insert lemma

And obtained the following new goals

Proof step 27:
validrefs(str, refs, ty, st), refs ≠ [] ⊦ ∃ sks. fits(refs .first, sks, st) ∧ st[refs .first -- sks] .refval = refs .last
Proof step 31:
∃ sks. fits((r1 ' + refs2) .first, sks, st) ∧ st[(r1 ' + refs2) .first -- sks] .refval = (r1 ' + refs2) .last, (r1 ' + refs2) .last = (r2 ' + refs1) .last, st[r2 -- sks] = refval((r2 ' + refs1) .last), fits(r2, sks, st), validrefs(str, r2 ' + refs1, st[r2 -- _type] .type, st), validrefs(str, r1 ' + refs2, st[r1 -- _type] .type, st), r2 ∈ refs, r1 ∈ refs, validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st), ∀ r, sks, r0, sks0. ¬ r ∈ refs ∨ ¬ r0 ∈ refs ∨ r = r0 ∨ ¬ fits(r, sks, st) ∨ ¬ fits(r0, sks0, st) ∨ st[r -- sks] ≠ st[r0 -- sks0] ∨ st[r -- sks] .refval = jvmref ⊦ (r2 ' + refs1) .last = jvmref, r1 = r2

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: ex-validrefs-fits antecedent: validrefs(str, refs, ty, st), refs ≠ [] succedent: ∃ sks. fits(refs .first, sks, st) ∧ st[refs .first -- sks] .refval = refs .last substlist: [str, refs, ty, st] → [str, r1 ' + refs2, st[r1 -- _type] .type, st] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, r1 ' + refs2, st[r1 -- _type] .type, st)]]