Step
*
of Lemma
cWO-induction
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[Q:T ⟶ ℙ]. TI(T;x,y.R[x;y];t.Q[t]) supposing cWO(T;x,y.R[x;y])
BY
{ xxx(UseWitness ⌜λf.fix((λF,t. (f t F)))⌝⋅ THEN RWO "cWO-induction-extract-sqequal" 0 THEN Auto)xxx }
Latex:
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[Q:T {}\mrightarrow{} \mBbbP{}]. TI(T;x,y.R[x;y];t.Q[t]) supposing cWO(T;x,y.R[x;y])
By
Latex:
xxx(UseWitness \mkleeneopen{}\mlambda{}f.fix((\mlambda{}F,t. (f t F)))\mkleeneclose{}\mcdot{} THEN RWO "cWO-induction-extract-sqequal" 0 THEN Auto)xxx
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