[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 35 from proof contains-levelsubset (previous step)

tys + ty0 ' = ty3 ' + tys1, level⊆(str, str0), contains(str, ty3 ' + tys1), type∃(str, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), ty0 ∈ tys1, ty3 ∈ tys, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ # tys1 .butlast < # tys, tys1 = [], contains(str0, ty, ty0), dups(tys), ty ∈ tys

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
tys + ty0 ' = ty3 ' + tys1, # tys < # tys1, ty3 ∈ tys, ty0 ∈ tys1, type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str, ty1), contains(str, ty3 ' + tys1), level⊆(str, str0), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys1 = [], ty ∈ tys, dups(tys), contains(str0, ty, ty0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m < 1 ↔ m = 0], [CSIMPSEQ : ⊦ # tys = 0 ↔ tys = []], [CSIMPSEQ : ⊦ tys ≠ [] → # tys .butlast = # tys - 1])]]