[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 24 from proof disjoint-def-pathex (previous step)

(r2 ' + refs2) .last = refs0 .last, validrefs(str, refs0, st[refs0 .first -- _type] .type, st), r2 ∈ refs, refs0 .first ∈ refs, validrefs(str, r2 ' + refs2, st[r2 -- _type] .type, st), ∀ r, r0, r1. ¬ r ∈ refs ∨ ¬ r0 ∈ refs ∨ r = r0 ∨ r1 = jvmref ∨ ¬ path∃(str, r, r1, st) ∨ ¬ path∃(str, r0, r1, st) ⊦ refs0 = [], r2 = refs0 .first, refs0 .last = jvmref

User applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
refs0 = r3 + refs1, (r2 ' + refs2) .last = refs0 .last, validrefs(str, refs0, st[r3 -- _type] .type, st), r2 ∈ refs, r3 ∈ refs, validrefs(str, r2 ' + refs2, st[r2 -- _type] .type, st), ∀ r, r0, r1. ¬ r ∈ refs ∨ ¬ r0 ∈ refs ∨ r = r0 ∨ r1 = jvmref ∨ ¬ path∃(str, r, r1, st) ∨ ¬ path∃(str, r0, r1, st) ⊦ refs0 = [], r2 = r3, refs0 .last = jvmref

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: references lemma-name: elim-1 antecedent: succedent: refs ≠ [] → (r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0) substlist: [refs, r, refs0] → [refs0, r3, refs1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ refs ≠ [] → ( r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0)])], [EXTRATERMS : (refs0, r3, refs1)]]