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Proof step 25 from proof sum-constant-countFun (previous step)

Σ countFun(i, j - 1, intfun) = (j - i) * intfun(j), 0 ≤ j, 0 ≤ i, i ≤ j, ∀ i1. i ≤ i1 ∧ i1 ≤ j → intfun(i1) = intfun(j), ∀ j0, i1, intfun, i0. i→n(j0) - i→n(i1) < i→n(j) - i→n(i) → (∀ i2. i1 ≤ i2 ∧ i2 ≤ j0 → intfun(i2) = i0) ∧ i1 ≤ j0 ∧ 0 ≤ i1 → Σ countFun(i1, j0, intfun) = (1 + j0 - i1) * i0 ⊦ (j - i) * intfun(j) + intfun(j) = (1 + j - i) * intfun(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: numsucc seq: ⊦ (* i0) * i + i = (i0 + 1) * i subst: [i, i0] → [intfun(j), j - i] flags: rewrite

Additional information

Used simplifier rules: sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: intfun(j), j - i