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Proof step 8 from proof middle-coef-larger-stronger (previous step)

4 ^ i = binom_coef(2 * i, i) * 2 * i, 0 ≤ 4 ^ i, 0 < i ⊦ binom_coef(2 * i, i) = 4 ^ i / (2 * i)

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: coef-zero: ⊦ 0 ≤ i → binom_coef(i, 0) = 1;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%div-mult-01: j ≠ 0, i0 ≠ 0 ⊦ (i * i0) / (j * i0) = i / j; from specification int-div%div-mult-num: j ≠ 0, j0 % j = 0 ⊦ (i * (* j0)) / (* j) = i * j0 / j; from specification int-div%one: ⊦ 1 * i = i; from specification int-mult