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Proof step 14 from proof elim-sub (previous step)

rational(i0, j0) = rational(i, j) + rational(~ i1, j1), 0 < j1, 0 < j0, 0 < j ⊦ rational(i, j) = rational(i0, j0) + rational(i1, j1)

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: rational-add-same: ⊦ rational(i, j) + rational(i1, j) = rational(i + i1, j);%add-zero-01: ⊦ rational(0, j1) + rational(i0, j0) = rational(i0, j0);%add-asso: ⊦ (ri + rj) + rj0 = ri + rj + rj0;%add-comm: ⊦ ri + rj = rj + ri;%equal-same: ⊦ 0 < j → (rational(i, j) = rational(i0, j) ↔ i = i0);% ⊦ ~ i + i = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;