[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 10 from proof orderedls-all (previous step)

n ≤ 1 + # y, ordered<(a0 ' + y), a < a0, m < n, m ≤ # y, ∀ m0, n0. m0 < n0 ∧ ¬ # y < n0 → (a0 ' + y)[m0] < (a0 ' + y)[n0] ⊦ (a ' + a0 ' + y)[m] < (a ' + a0 ' + y)[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ x ≠ [] ∧ n ≠ 0 → x[n] = x.rest[n - 1]
Proof step 12:
¬(a ' + a0 ' + y ≠ [] ∧ m ≠ 0), n ≤ 1 + # y, ordered<(a0 ' + y), a < a0, m < n, m ≤ # y, ∀ m0, n0. m0 < n0 ∧ ¬ # y < n0 → (a0 ' + y)[m0] < (a0 ' + y)[n0] ⊦ (a ' + a0 ' + y)[m] < (a ' + a0 ' + y)[n]
Proof step 22:
a ' + a0 ' + y ≠ [] ∧ m ≠ 0, n ≤ 1 + # y, ordered<(a0 ' + y), a < a0, m < n, m ≤ # y, ∀ m0, n0. m0 < n0 ∧ ¬ # y < n0 → (a0 ' + y)[m0] < (a0 ' + y)[n0] ⊦ (a ' + a0 ' + y).rest[m - 1] < (a ' + a0 ' + y)[n]

Rule argument

spec: list-del inst: name: get-rec seq: ⊦ x ≠ [] ∧ n ≠ 0 → x[n] = x.rest[n - 1] subst: [n, x] → [m, a ' + a0 ' + y] flags: rewrite

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: m, a ' + a0 ' + y