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Proof step 28 from proof lastn-fill-sgn (previous step)

# bits0 = # fillsgn(# bits0, sgn(true ' + bits0)), 1 + # sgn(true ' + bits0) < # bits1 + # bits0, # sgn(true ' + bits0) < # bits0, # sgn(true ' + bits0) < # bits1 + # bits0, true ∈ bits1 ⊦ fillsgn(# bits0, sgn(true ' + bits0)) = bits0, bits0 = [], bits1 = [], bits1 + bits0 = [], false ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)
Proof step 30:
¬(bits0 ≠ [] ∧ (bits0.first ↔ true)), # bits0 = # fillsgn(# bits0, sgn(true ' + bits0)), 1 + # sgn(true ' + bits0) < # bits1 + # bits0, # sgn(true ' + bits0) < # bits0, # sgn(true ' + bits0) < # bits1 + # bits0, true ∈ bits1 ⊦ fillsgn(# bits0, sgn(true ' + bits0)) = bits0, bits0 = [], bits1 = [], bits1 + bits0 = [], false ∈ bits1
Proof step 32:
bits0 ≠ [] ∧ (bits0.first ↔ true), # bits0 = # fillsgn(# bits0, sgn(bits0)), 1 + # sgn(bits0) < # bits1 + # bits0, # sgn(bits0) < # bits0, # sgn(bits0) < # bits1 + # bits0, true ∈ bits1 ⊦ fillsgn(# bits0, sgn(bits0)) = bits0, bits0 = [], bits1 = [], bits1 + bits0 = [], false ∈ bits1

Rule argument

name: sgn-rec-01 rotate: F subst: [bits, boolvar] → [bits0, true]

Additional information

Used terms: bits0, true