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Proof step 5 from proof div-div-pred-01 (previous step)

i < 0 ⊦ (((i - 1) / 2 - 1) / 2 - 1) / 2 = (i - 7) / 8

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i < 0 → ((i - 1) / 2 - 1) / 2 = (i - 3) / 4
Proof step 7:
i < 0, (i - 1) / 2 < 0 ⊦ ((i - 1) / 2 - 3) / 4 = (i - 7) / 8

Rule argument

spec: <toplevel> name: div-div-pred seq: ⊦ i < 0 → ((i - 1) / 2 - 1) / 2 = (i - 3) / 4 subst: [i] → [(i - 1) / 2] flags: <all paths>

Additional information

Used simplifier rules: div-ls-zero: 0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0;% ⊦ i + (j - i0) = i + j - i0; (s)% ⊦ (* i) + i0 - (* j) = (i - j) + i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; (s)% ⊦ i ≤ ~1 ↔ i < 0; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: (i - 1) / 2