[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 60 from proof multg-at-ref (previous step)

2 ≤ i0, i→n(i0 * (countrefs2(ints2) + 1)) ≤ # refs, 0 ≤ i0, 0 < i0, ∀ sk, i, ints0, st, ty, r0, r, refs, ints1. ints#(ints1) < ints#(i0 + ints2) → (i→n(countrefs2(ints1)) ≤ # refs → r = r0 ∨ (addarraymultlist(r, ty, st, refs, ints1, ints0, i)[r0 -- sk]) = st[r0 -- sk] ∨ r0 ∈ refs) ⊦ r = r0, ints2 = [], (addarraymultlist (refs .first, ty, addarraymultlist (r, ty, st[r -- (i0 - 1) ', refval(refs .first)][r -- _type, typeval(mktype_from_dims(ty, (1 + n→i(# ints2)) + i))][r -- _length, intval(ints0 .first)], refs .rest, (i0 - 1) ' + ints2, ints0, i), restn(i→n(countrefs2((i0 - 1) ' + ints2)), refs .rest), ints2, ints0 .rest, i) [r0 -- sk ] ) = st[r0 -- sk], r0 ∈ refs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
⊦ ¬ countrefs2(ints) < 0
Proof step 59:
refs = r1 + refs0 ∧ refs ≠ [], 2 ≤ i0, i→n(i0 * (countrefs2(ints2) + 1)) ≤ # refs, 0 ≤ i0, 0 < i0, ∀ sk, i, ints0, st, ty, r0, r, refs, ints1. ints#(ints1) < ints#(i0 + ints2) → (i→n(countrefs2(ints1)) ≤ # refs → r = r0 ∨ (addarraymultlist(r, ty, st, refs, ints1, ints0, i)[r0 -- sk]) = st[r0 -- sk] ∨ r0 ∈ refs) ⊦ r = r0, ints2 = [], (addarraymultlist (r1, ty, addarraymultlist (r, ty, st[r -- (i0 - 1) ', refval(r1)][r -- _type, typeval(mktype_from_dims(ty, (1 + n→i(# ints2)) + i))][r -- _length, intval(ints0 .first)], refs0, (i0 - 1) ' + ints2, ints0, i), restn(i→n(countrefs2((i0 - 1) ' + ints2)), refs0), ints2, ints0 .rest, i) [r0 -- sk ] ) = st[r0 -- sk], r0 ∈ refs

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs, r1, refs0] ,T ,list-data ,references ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # [] = 0], [CSIMPFORWARD : ⊦ i < ((* j)) ∧ j < 0 → i < 0], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j)], [CSIMPSEQ : 0 ≤ i ⊦ i→n(i) ≤ ((* m)) ↔ i ≤ n→i(m)], [CSIMPSEQ : ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0)], [CSIMPSEQ : ⊦ i + ((* j)) ≤ ((* j0)) ↔ i ≤ j0 - j], [CSIMPSEQ : ⊦ i ≤ (~1) ↔ i < 0], [CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs, r1, refs0)]]