[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 40 from proof disjoint-def-fits (previous step)

refs1 .last = refs0 .last, refs1 .first ∈ refs, refs0 .first ∈ refs, validrefs(str, refs1, st[refs1 .first -- _type] .type, st), validrefs(str, refs0, st[refs0 .first -- _type] .type, st), 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 ⊦ refs1 = [], refs0 = [], refs1 .first = refs0 .first, refs0 .last = jvmref

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 39:
refs1 = r1 + refs2, refs1 .last = refs0 .last, r1 ∈ refs, refs0 .first ∈ refs, validrefs(str, refs1, st[r1 -- _type] .type, st), validrefs(str, refs0, st[refs0 .first -- _type] .type, st), 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 ⊦ refs1 = [], refs0 = [], r1 = refs0 .first, refs0 .last = jvmref

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: references lemma-name: elim-list-c antecedent: refs ≠ [] succedent: r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 substlist: [refs, r, refs0] → [refs1, r1, refs2] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs1, r1, refs2)]]