Nuprl Lemma : decidable__node_complete
∀n:node. ((∀x,y:Prop. Dec(x = y ∈ Prop)) ⇒ Dec(node_complete{i:l}(n)))
Proof
Definitions occuring in Statement :
node_complete: node_complete{i:l}(n),
node: node,
dl-prop: Prop,
decidable: Dec(P),
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
node_complete: node_complete{i:l}(n),
uall: ∀[x:A]. B[x],
member: t ∈ T,
node: node,
top: Top,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
pi2: snd(t),
pi1: fst(t),
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
decidable__cand,
l_all_wf2,
dl-prop_wf,
pi1_wf_top,
list_wf,
istype-void,
dl-localT_wf,
dl-prop-obj_wf,
l_member_wf,
dl-localF_wf,
decidable__l_all-better-extract,
decidable__l_member,
decidable_wf,
equal_wf,
node_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
productElimination,
independent_pairEquality,
hypothesisEquality,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
lambdaEquality_alt,
applyEquality,
dependent_functionElimination,
setElimination,
rename,
setIsType,
universeIsType,
because_Cache,
inhabitedIsType,
independent_functionElimination,
functionIsType
Latex:
\mforall{}n:node. ((\mforall{}x,y:Prop. Dec(x = y)) {}\mRightarrow{} Dec(node\_complete\{i:l\}(n)))
Date html generated:
2020_05_20-AM-09_02_07
Last ObjectModification:
2019_11_27-PM-02_29_42
Theory : dynamic!logic
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