Nuprl Lemma : not-not-sig-to-W
∀A:Type. ∀B:A ⟶ Type. ((∀R:Type. (((a:A × (B[a] ⇒ R)) ⇒ R) ⇒ R)) ⇒ W(A;a.B[a]))
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_apply: x[s],
so_lambda: λ2x.t[x],
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
istype-universe,
W_wf,
W-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
sqequalRule,
Error :functionIsType,
Error :inhabitedIsType,
hypothesisEquality,
Error :productIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
Error :universeIsType,
applyEquality,
universeEquality,
dependent_functionElimination,
Error :lambdaEquality_alt,
independent_functionElimination,
because_Cache,
rename,
productElimination
Latex:
\mforall{}A:Type. \mforall{}B:A {}\mrightarrow{} Type. ((\mforall{}R:Type. (((a:A \mtimes{} (B[a] {}\mRightarrow{} R)) {}\mRightarrow{} R) {}\mRightarrow{} R)) {}\mRightarrow{} W(A;a.B[a]))
Date html generated:
2019_06_20-PM-00_36_41
Last ObjectModification:
2018_10_06-AM-11_20_24
Theory : co-recursion
Home
Index