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Proof step 7 from proof int2bits-2pot-03 (previous step)

uint2bits(j) = false ' + true ' + bits, 0 ≤ j ⊦ 2 ^ n→i(# uint2bits(j).rest) = j + 1, false ∈ uint2bits(j).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ false ∈ bits ∧ 0 ≤ i → (uint2bits(i) = false ' + true ' + bits ↔ i = 2 ^ (n→i(# bits) + 1) - 1)
Proof step 9:
¬(¬ false ∈ bits ∧ 0 ≤ j), uint2bits(j) = false ' + true ' + bits, 0 ≤ j ⊦ 2 ^ n→i(# uint2bits(j).rest) = j + 1, false ∈ uint2bits(j).rest

Rule argument

name: uint2bits-2pot-04 rotate: F subst: [bits, i] → [bits, j]

Additional information

Used simplifier rules: uint2bits-2pot-02: 0 < i ⊦ uint2bits(2 ^ i - 1) = false ' + mklist(true, i→n(i));% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 ≤ n→i(n);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i→n(n→i(n) + 1) = n + 1;% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ ¬ false ∈ bits → mklist(true, # bits) = bits;% ⊦ mklist(boolvar, 1) = boolvar ';% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ i + (j - i) = j; Used terms: bits, j