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Proof step 5 from proof abs-succ (previous step)

~1 = i + j, i < 0, j < 0 ⊦ j = 0

User applied rule cut formula

And closed the goal!

Rule argument

fma: i = ~ j - 1

Additional information

Used simplifier rules: Minus-def: ⊦ ~ i = 0 - i;%sub-sub: ⊦ i - j - i0 = i - j + i0;%num-subadd: ⊦ (* i) - j + (* i0) = i - i0 - j;%sub-add-01: ⊦ i + (j - i0) = i + j - i0;%mone-01: ⊦ i + ~1 = i - 1;%sub-add-09: ⊦ i - j + i = ~ j;%sub-ls: ⊦ i - j < i0 ↔ i < j + i0;%mone-06: ⊦ ~1 < i ↔ 0 ≤ i;%lels-03: ⊦ i < j → (j ≤ i ↔ false);%Minus-def: ⊦ ~ i = 0 - i;%sub-sub: ⊦ i - j - i0 = i - j + i0;%num-subadd: ⊦ (* i) - j + (* i0) = i - i0 - j;%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 + i = i; (s) Used formulas: i = ~ j - 1