[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 45 from proof validrefs-put-notin (previous step)

acc = r1 + refs, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r, sk, val. (validrefs(str, acc, ty, st[r -- sk, val]) ↔ validrefs(str, acc, ty, st)) ∨ r ∈ acc ⊦ r0 = jvmref, r = r0, (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st[r -- sk, val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st)), acc = [], r ∈ acc

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st0, r2, sk0, val0. (validrefs(str0, r1 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, r1 ' + refs, ty0, st0)) ∨ r2 = r1 ∨ r2 ∈ refs ⊦ r0 = jvmref, r = r0, (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- sk, val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st)), r = r1, r ∈ refs

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]