[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 4 from proof sum-equal (previous step)

1 + # ints1 = # ints0, ∀ ints0. # ints1 = # ints0 ∧ (∀ n. n < # ints0 → ints1[n] = ints0[n]) → Σ ints1 = Σ ints0, ∀ n. n < # ints0 → (i ' + ints1)[n] = ints0[n] ⊦ i + Σ ints1 = Σ ints0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ints ≠ [] → Σ ints = ints.first + Σ ints.rest
Proof step 6:
ints0 ≠ [], 1 + # ints1 = # ints0, ∀ ints0. # ints1 = # ints0 ∧ (∀ n. n < # ints0 → ints1[n] = ints0[n]) → Σ ints1 = Σ ints0, ∀ n. n < # ints0 → (i ' + ints1)[n] = ints0[n] ⊦ i + Σ ints1 = ints0.first + Σ ints0.rest

Rule argument

spec: inst: name: sum-rec-01 seq: ⊦ ints ≠ [] → Σ ints = ints.first + Σ ints.rest subst: [ints] → [ints0] flags: rewrite, current

Additional information

Used simplifier rules: size-01: ⊦ # [] = 0; from specification list-data[intlista]%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: ints0