[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 36 from proof nonnullrefs-dups-firstoc (previous step)

val ' + vals0 = vals2 + refval(r) ' + vals1 + refval(r) ' + vals, ¬ is_referencevalue(val) ∨ val .refval = jvmref ⊦ r = jvmref, refval(r) ∈ vals2, refval(r) ∈ vals1, dups(vals0 .nonnullrefs), ∃ r, vals, vals1, vals2. vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1, ¬ val ∈ vals2 ∧ val ≠ refval(r) ∧ ¬ val ∈ vals1 ∧ ¬ val ∈ vals

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
vals ≠ [] ⊦ val ' + vals0 = vals + vals1 ↔ val = vals .first ∧ vals0 = vals .rest + vals1
Proof step 35:
vals2 ≠ [], val = vals2 .first ∧ vals0 = vals2 .rest + refval(r) ' + vals1 + refval(r) ' + vals, ¬ is_referencevalue(val) ∨ val .refval = jvmref ⊦ r = jvmref, refval(r) ∈ vals2, refval(r) ∈ vals1, dups(vals0 .nonnullrefs), ∃ r, vals, vals1, vals2. vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1, ¬ val ∈ vals2 ∧ val ≠ refval(r) ∧ ¬ val ∈ vals1 ∧ ¬ val ∈ vals

Rule argument

[x0lemmaarg: spec-name: list instance-name: javavalues lemma-name: firsteq antecedent: vals ≠ [] succedent: val ' + vals0 = vals + vals1 ↔ val = vals .first ∧ vals0 = vals .rest + vals1 substlist: [vals1, vals, vals0, val] → [refval(r) ' + vals1 + refval(r) ' + vals, vals2, vals0, val] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, javavalues, Nil, ⊦ [] + vals = vals], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : list, javavalues, c-06, ⊦ val ' + vals = val0 ' + vals0 ↔ val = val0 ∧ vals = vals0], [CSIMPNAMEDSEQ : list, javavalues, in-empty, ⊦ ¬ val ∈ []], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r])], [EXTRATERMS : (refval(r) ' + vals1 + refval(r) ' + vals, vals2, vals0, val)]]