Nuprl Lemma : decidable__implies_better
∀[P:ℙ]. ∀Q:⋂x:P. ℙ. (Dec(P) ⇒ (P ⇒ Dec(Q)) ⇒ Dec(P ⇒ Q))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
isect: ⋂x:A. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
exists: ∃x:A. B[x]
Lemmas referenced :
decidable__implies,
decidable_wf,
isect_subtype_rel_trivial,
subtype_rel_weakening,
ext-eq_weakening,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
because_Cache,
functionEquality,
applyEquality,
instantiate,
cumulativity,
sqequalRule,
universeEquality,
lambdaEquality,
independent_isectElimination,
dependent_pairFormation,
isectEquality
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}Q:\mcap{}x:P. \mBbbP{}. (Dec(P) {}\mRightarrow{} (P {}\mRightarrow{} Dec(Q)) {}\mRightarrow{} Dec(P {}\mRightarrow{} Q))
Date html generated:
2016_05_15-PM-03_37_42
Last ObjectModification:
2015_12_27-PM-01_15_27
Theory : general
Home
Index