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Proof step 26 from proof short-law-righthift-not (previous step)

i2s(16384) = i2s (bits2int (sublist (0, # fillsgn (32, true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false '), false ' + fillsgn (32, true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ')))) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 28:
# ( true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ') ≤ 32 ∧ true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' ≠ [], i2s(16384) = i2s (bits2int (sublist (0, # ( mklist (( true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' ).first, 32 - # ( true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ')) + true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false '), false ' + mklist (( true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' ).first, 32 - # ( true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ')) + true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false '))) ⊦

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [ true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ', 32] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ []; Used terms: true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ', 32