Nuprl Lemma : W-to-not-not-sig2
∀A:Type. ∀B:A ⟶ Type. (W(A;a.B[a]) ⇒ (∀R:Type. (((a:A × (B[a] ⇒ R)) ⇒ R) ⇒ R)))
Proof
Definitions occuring in Statement :
W: W(A;a.B[a]),
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
W_wf,
W-induction,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
cumulativity,
universeEquality,
rename,
instantiate,
productEquality,
independent_functionElimination,
dependent_functionElimination,
introduction,
dependent_pairEquality
Latex:
\mforall{}A:Type. \mforall{}B:A {}\mrightarrow{} Type. (W(A;a.B[a]) {}\mRightarrow{} (\mforall{}R:Type. (((a:A \mtimes{} (B[a] {}\mRightarrow{} R)) {}\mRightarrow{} R) {}\mRightarrow{} R)))
Date html generated:
2016_05_14-AM-06_17_39
Last ObjectModification:
2015_12_26-PM-00_03_39
Theory : co-recursion
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